the count in a bacteria culture was 900 after 20 minutes and 1100 after 35 minutes. assuming the count grows exponentially,
What was the initial size of the culture?
Find the doubling period.
Find the population after 60 minutes.
When will the population reach 15000.

Answers

Answer 1

The population will reach 15,000 after approximately 156.24 minutes.

To find the initial size of the culture, we can use the exponential growth formula:

[tex]N = N0 * e^(rt)[/tex]

Where:

N = final count after a certain time

N0 = initial count

r = growth rate

t = time in minutes

e = Euler's number (approximately 2.71828)

We are given two data points:

At 20 minutes: N = 900

At 35 minutes: N = 1100

Using these points, we can set up two equations:

[tex]900 = N0 * e^(20r) ---(1)[/tex]

[tex]1100 = N0 * e^(35r) ---(2)[/tex]

To solve this system of equations, we can divide equation (2) by equation (1):

[tex]1100 / 900 = (N0 * e^(35r)) / (N0 * e^(20r))[/tex]

Simplifying:

[tex]1.2222 = e^(35r) / e^(20r)[/tex]

[tex]e^(a - b) = e^a / e^b:[/tex]

[tex]1.2222 = e^((35-20)r)[/tex]

Taking the natural logarithm (ln) of both sides:

[tex]ln(1.2222) = ln(e^((35-20)r))[/tex]

ln(1.2222) = (35-20)r

Now we can solve for r:

r = ln(1.2222) / 15

Using a calculator, we find:

r ≈ 0.0461

Now we can substitute the value of r into equation (1) to find N0:

[tex]900 = N0 * e^(20 * 0.0461)[/tex]

[tex]N0 = 900 / e^(0.922)[/tex]

N0 ≈ 697.86

Therefore, the initial size of the culture was approximately 697.86.

To find the doubling period, we can use the formula:

doubling period = ln(2) / r

doubling period = ln(2) / 0.0461

Using a calculator, we find:

doubling period ≈ 15.03 minutes

Therefore, the doubling period is approximately 15.03 minutes.To find the population after 60 minutes, we can use the formula:

[tex]N = N0 * e^(rt)[/tex]

[tex]N = 697.86 * e^(0.0461 * 60)[/tex]

Using a calculator, we find:

N ≈ 1579.83

Therefore, the population after 60 minutes is approximately 1579.83.

To find when the population will reach 15,000, we can rearrange the formula:

[tex]N = N0 * e^(rt)[/tex]

15,000 = N0 [tex]* e^(0.0461 * t)[/tex]

Dividing both sides by N0 and taking the natural logarithm:

ln(15,000/N0) = 0.0461 * t

Now we can solve for t:

t = ln(15,000/N0) / 0.0461

Substituting the value of N0 we found earlier:

t = ln(15,000/697.86) / 0.0461

Using a calculator, we find:

t ≈ 156.24 minutes

Therefore, the population will reach 15,000 after approximately 156.24 minutes.

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Related Questions

If p(x)= 2^x, what is the value of p(3) - p(2)?

Answers

Answer:

4

Step-by-step explanation:

p(3) = 2³ = 8

p(2) = 2² = 4

8-4 = 4

An experiment was performed to test whether caffeine in Coca-Cola would improve performance on an intelligence test. One randomly chosen group of subjects was given an 8 oz. cup of Coca-Cola containing caffeine to drink 10 minutes before taking the intelligence test. Another randomly chosen group was given an 8 oz. cup of decaffeinated Coke to drink 10 minutes before taking the test. Neither group had any food or drink for three hours before the experiment began. What are the levels or conditions of the independent variable

Answers

Answer:

8 oz of cocacola drink containing caffeine

8 oz of Decaffeinated Coke

Step-by-step explanation:

Th independent variables is that variable which causes a change in the output or the dependent or response variable. In the scenario described above, the type of drink Given to the participants is the independent variable

The Independent variable is the type of drink Given to the subjects with two levels ;

Levels :

cocacola drink containing caffeine

Decaffeinated Coke

Therefore, we can conclude that, there are two levels Of the jndependent variable, which are stated above.

Show all steps please!

Suppose you are told that 3.59% of Wendigos are less than 273cm tall while only 4.01% are taller than 326.25 cm tall. Find the mean and standard deviation of the heights of Wendigos.

Answers

The mean of the heights of Wendigos ≈ 302.523 cm, and the standard deviation ≈ 14.165 cm.

To obtain the mean and standard deviation of the heights of Wendigos, we can use the information given about the percentiles.

Let's denote the mean as μ and the standard deviation as σ.

Step 1: Finding the Z-scores

First, we need to find the Z-scores corresponding to the given percentiles.

For the lower percentile:

Z = (X - μ) / σ = -1.880

For the upper percentile:

Z = (X - μ) / σ = 1.880

Step 2: Finding the corresponding values using Z-scores

Next, we need to find the values corresponding to the Z-scores using a standard normal distribution table or a calculator.

For the lower percentile:

Z = -1.880 corresponds to a cumulative probability of 0.0359

For the upper percentile:

Z = 1.880 corresponds to a cumulative probability of 0.9601

Step 3: Calculating the values

Using the cumulative probabilities obtained, we can find the corresponding values.

For the lower percentile:

X = Z * σ + μ

273 = -1.880 * σ + μ

For the upper percentile:

X = Z * σ + μ

326.25 = 1.880 * σ + μ

Step 4: Solving the equations

We now have a system of equations with two unknowns (μ and σ).

273 = -1.880 * σ + μ   (Equation 1)

326.25 = 1.880 * σ + μ   (Equation 2)

We can solve this system of equations to find the values of μ and σ.

Subtracting Equation 1 from Equation 2, we get:

326.25 - 273 = 1.880 * σ + μ - (-1.880 * σ + μ)

53.25 = 3.760 * σ

Dividing both sides by 3.760, we get:

σ ≈ 14.165

Substituting this value of σ into Equation 1, we can solve for μ:

273 = -1.880 * 14.165 + μ

273 + 1.880 * 14.165 = μ

μ ≈ 302.523

Therefore, mean is approximately 302.523 cm, and the standard deviation is approximately 14.165 cm.

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y−3=5(x−2) what is the slope?

Answers

Answer:

y=5(x-2)+3 or y= 5x+7

Step-by-step explanation:

Martina runs 6 miles in 50 minutes. At the same rate, how many miles would she run in 35 minutes?

Answers

It may be 45 I think

Answer:

4.2 miles

Step-by-step explanation:

Martina runs 6 miles in 50 minutes, we have to find the rate at which she is running. Put it in a fraction [tex]\frac{6}{50}[/tex] or she runs 6 miles every 50 minutes. When we divide we get that she is running, 0.12 miles evrey minute. The question askes us how far Matina will run in 35 minutes, so we multiply 0.12 by 35, and we get that she will run 4.2 miles.

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A single number cube is rolled twice and the two numbers are added.


PART A:

How can you determine the total number of possible outcomes

Answers

Answer:

well if you where talking about the dice the awnser is 6 and if you are tlking about the shirts then you can do 3 times 3 i thik is the right awnser

Step-by-step explanation:

1. a dice is a cube a cube has 6 sides a single number dice is a dice that only has numbers that are by themselves so the awnser can only be on the dice 6 to 9 so now we know that it is 6 now 6 times 2 is 12 because it got rolled twice

2.

What is the value of x in the equation below?
12 – 2(x-1)=6

Answers

X=25 in this equation. But if u divide by 12 it’s -25
X=-2
You would distribute the -2 and Zoe 1 and 1*-2=-2



Stop and Shop sells 6 cases of Pepsi for $21.60. What is the constant of proportionality?

Answers

Answer: $3.60 per case

Step-by-step explanation: $21.60 divided by 6 = 3.60

Find the potential function f for the field F.
F = -1/x i+1/y j-1/z k

Answers

The potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.

Given field is F = (-1/x) i+ (1/y) j- (1/z) k

The potential function f is given by

∂f/∂x = -1/x .........(1)∂f/∂y = 1/y .........(2)∂f/∂z = -1/z .........(3)

Using the equation (1)

we get

f = -ln |x| + C1

Using the equation (2)

we get

f = ln |y| + C2

Using equation (3) we get

f = -ln |z| + C3

On adding the above three equations we get

f = ln |y| - ln |z| - ln |x| + C

where C = C1 + C2 + C3 is a constant of integration.

Therefore, the potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.

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If there is 0.25 probability that a child in New York gets the flu and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu?If there is 0.25 probability that a child in New York gets the file and a 0.30 probability that a child in Los Angeles gets the flu, what is the probability that both will get the flu? O 0.075 O 0.275 O 0.25 O 0.55

Answers

Answer:

(.25)(.30) = .075 probability that both children will get the flu

The probability that both a youngster in New York and a kid in Los Angeles will get this season's virus can be determined by duplicating the singular probabilities. Consequently, the likelihood that both will get influenza is 0.075.

To find the probability of the two occasions happening, we duplicate the probabilities of every occasion. Considering that the probability of a kid in New York getting this season's virus is 0.25 (or 25%) and the probability of a youngster in Los Angeles getting influenza is 0.30 (or 30%), we multiply these probabilities: 0.25 * 0.30 = 0.075. This implies there is a 0.075 probability, or 7.5%, that both a youngster in New York and a kid in Los Angeles will get influenza.

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The mean score in a physics test is 75% with the standard deviation 6.5%. Suppose that the scores in the test are approximately normally distributed. What is the probability that a randomly selected student scores more than 82%? Round your answer for 4 decimal places.

__________

Answers

The probability that a randomly selected student scores more than 82% on the physics test, we can use the standard normal distribution and the given mean and standard deviation.

The z-score formula is given by z = (x - μ) / σ, where z represents the z-score, x is the observed value, μ is the mean, and σ is the standard deviation. In this case, the observed value is 82%, the mean is 75%, and the standard deviation is 6.5%. Plugging these values into the formula, we calculate the z-score as z = (0.82 - 0.75) / 0.065 = 1.0769.

Next, we need to find the area to the left of the z-score in the standard normal distribution table or using a calculator. The area to the left of 1.0769 corresponds to the probability of scoring less than 82%. Let's assume this area is P(z < 1.0769).

The probability of scoring more than 82%, we subtract P(z < 1.0769) from 1: P(z > 1.0769) = 1 - P(z < 1.0769).

Using a standard normal table or a calculator, we can find P(z < 1.0769) to determine the probability.

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A woman bought a bag of rice 5700 naira and in 3 weeks later, she could only buy 2/4 of the bags for 5700 naira. Find the percentage?

Answers

Answer: 100% increase

Step-by-step explanation:

You need the find the cost per bag in those weeks.

Three weeks ago, she could buy a bag for N5,700.

Three weeks after that, she could only buy half a bag for the same amount. A bag therefore costs:

= 5,700 ÷ 2/4

= N11,400

The percentage increase is:

= (11,400 - 5,700) / 5,700

= 100%

A person visits the store and picks up five kg vegetables for did he buy?
£6.25. Which vegetable
Tomato - £1.50 per kg Carrot - £1.75 per kg Cabbage - £2 per kg Beetroot - £1.25 per kg

Answers

the answer is beetroot

Which number line shows - graphed?

Answers

Answer:

The second one down is the answer

Step-by-step explanation:

A birthday cake is being made using a cylindrical baking pan. The radius of the pan is 4 inches, and the height is 5 inches.

Which formula represents the correct way to calculate the volume of the cake?

O V = (4)(5)

O V = r(4)(5)

O V = $(5) (4)

O V = $(4)?(5)

Answers

Answer:

the formula represent the correct way is  π(4)^2 (5)

Step-by-step explanation:

The formula that represent the correct way to calculate is given below:

As we know that

Volume = πr^2 h

where

r denotes the radius i.e. 4 inches

And, h denotes the height i.e. 5 inches

Now placed these values to the above formula

So,

= π(4)^2 × 5

= 80π in^3

Hence, the formula represent the correct way is  π(4)^2 (5)

Answer: the answer is D.

Step-by-step explanation:

Factor 9z^2 - 6x +1.
pls will mark you brainiest

Answers

Answer:

It is not factorable

Step-by-step explanation:

The expression is not factorable with rational numbers.

Answer:

This is not factorable.

Step-by-step explanation:

This is not factorable.

One hundred tickets, numbered 1, 2, 3, …, 100, are sold to 100 people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). How many ways are there to award the prizes if a) the person holding ticket 47 wins one of the prizes? b) the people holding tickets 19 and 47 both win prizes?

Answers

Solution :

It is given that four different prizes were awarded. So,

a). 4 ways for person 47 to win a prize

     99 ways to give out the 2nd prize

     98 ways to give the 3rd prize

      97 ways to give the last prize

     ∴  P(99,3) = 99 x 98 x 97

b). 1 way to give person 47 their prize

    1 way to give person 19 their prize

    98 ways to give out the 3rd prize

    97 ways to give out the last prize

    So, P(98,2) = 98 x 97

answer easy question quick ​

Answers

Answer:

Step-by-step explanation:

a) 9.80- 98/10

b) 7.3- 73/10

a) 7/100- 0.07

b) 82/10- 8.2

Hope this helps

Fraction:

a) 98/100

b) 73/10

Decimal:

a) 0.07

b) 8.2

Will Mark Brainliest To First Correct Answer.
Properties of Kites on IXL. I Only need to get one more correct and dont want to get reset...

Answers

Step-by-step explanation:

[tex]ei = \sqrt{ {45}^{2} - {27}^{2} } = \\ = \sqrt{2025 - 729} = \\ = \sqrt{1296} = \\ = 36[/tex]

Should i trust the links people say "Their is an imagine in this link that contains the answer" usually these links are from sus profiles. So should i use it or no?​

Answers

Answer:

no don't ever click on links okay.

Step-by-step explanation:

MARKING BRAINLIEST TO FIRST PERSON WHO IS CORRECT!


I need help with #13

Answers

Answer:

True

False

False

Step-by-step explanation:

A recent stocktake measured the price of BBQs at a large hardware store. From the stocktake, it was determined that the price was normally distributed with a mean of 500 dollars and a standard deviation of 50 dollars. Twenty per cent of the BBQs would cost more than what price? Select from the answers below.

575.5

542

526

459

Answers

The price at which twenty percent of the BBQs would cost more is $542 and it follows a normal distribution.

In this case, we are given that the price of BBQs at a large hardware store follows a normal distribution with a mean of $500 and a standard deviation of $50. We want to find the price at which twenty percent of the BBQs would cost more.

To solve this problem, we need to find the value, denoted as x, for which 20% of the BBQs are priced higher. This can be done by finding the z-score corresponding to the 20th percentile and then converting it back to the original scale.

The z-score is calculated using the formula:

z = (x - μ) / σ,

where μ is the mean and σ is the standard deviation.

To find the z-score corresponding to the 20th percentile, we can use a standard normal distribution table or a statistical calculator. The z-score corresponding to the 20th percentile is approximately -0.84.

Now we can use the z-score to find the corresponding value in the original scale:

-0.84 = (x - 500) / 50.

Solving for x, we get:

-0.84 * 50 = x - 500,

-42 = x - 500,

x = 500 - 42,

x = 458.

So, twenty percent of the BBQs would cost more than $458. However, since we need to choose from the given options, the closest price to $458 is $459.

Therefore, the answer is $459.

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Your parents gave you $0.35 on Sunday and then gave you twice as much money on Monday as they did on Sunday. On Tuesday, they gave you twice as much money as they gave you monday. The pattern continued for a week. How much money did your parents give you on Saturday??

Answers

Answer:

$22.40 im pretty sure its right

Step-by-step explanation:

sorry if im late and mark me brainliest if im right

What is your dream career and why ?

Answers

Answer:

Step-by-step explanation:

Professional dancers cause I’ve danced since I was 3 and I’ve always wanted to do it. And I wanna model on the side

Answer:

Detective/Forensics scientist

Step-by-step explanation:

I want to be a detective/ forensic scientist because I am interested in science and investigating.

PLEASE HELP ME ASAP I SWEAR IT WOULD BE A BIG HELP.
Jethro has sat 5 tests.
Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74
Jethro has to sit one more test that is also to be marked out of 100
Jethro wants his mean mark for all 6 tests to be at least 77
Work out the least mark that Jethro needs to get for the last test. ​

Answers

This paper will discuss the mathematics involved in determining the least mark that Jethro needs to get for the last test in order to end up with a mean mark of 77 over all 6 tests.

Jethro has sat 5 tests and each test was marked out of 100. Therefore, Jethro’s marks for the 5 tests can be represented by x1, x2, x3, x4, and x5. Jethro’s mean mark for the 5 tests is 74, which can be represented by the mathematical equation: (x1 + x2 + x3 + x4 + x5) / 5 = 74.

Jethro needs to sit one more test that is also marked out of 100 and he wants his mean mark for all 6 tests to be at least 77. Therefore, the least mark that Jethro needs to get for the last test can be found by rearranging the equation to: (x1 + x2 + x3 + x4 + x5 + x6) / 6 = 77. This can be written in its simplified form as: 6x6 = 77(x1 + x2 + x3 + x4 + x5).

In order to find the least mark that Jethro needs to get for the last test, x6, the other terms must be known. Since Jethro has already sat the 5 tests the marks for these tests are known, so they can be added together. This results in: x6 = 77(x1 + x2 + x3 + x4 + x5) / 6. Therefore, Jethro needs to get a mark of at least 77.6 (rounded to the nearest tenth) on the last test in order to end up with a mean mark of 77.

Mother put 22 apples in each basket. How many baskets did she use for 390 apples?

Answers

Answer:

To find the no. of baskets used to put 390 apples we have to divide 390/22  which is 17.7272727273,

so to put 390 apples we need approximately 18 baskets.

hope this answer helps you...

answer: 17.72
solution: probably 17 bc there’s not enough for 18

In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , what is the next permutation after GAEDBHFC? (Assume the usual alphabetic order of letters.)
a. HAEFBDCG b. GAEDCBFH c. DEHBFGCA d. None of the other answers is correct. e. FDAEGBCH

Answers

In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , the next permutation after GAEDBHFC will be GAEDBHFD.

What is lexicographic ordering?

Lexicographic ordering or dictionary ordering is a way of ordering elements based on their alphabetical or numerical values.

To find the next permutation in the lexicographic ordering, we need to find the smallest possible permutation that is greater than GAEDBHFC by considering the order of the letters.

Let's analyze the given permutation:

GAEDBHFC

To find the next permutation, we start from right to left and look for the first occurrence of a letter that can be replaced by a greater letter. In this case, the first such occurrence is "C" (after "H").

Next, we need to find the smallest letter that is greater than "C" from the remaining letters. From the letters {C, D, E, F, G, H}, the smallest greater letter than "C" is "D".

Now, we swap "C" with "D":

GAEDBHFD

After swapping, we need to sort the remaining letters in ascending order to obtain the smallest permutation. The remaining letters are {B, E, F, G, H}. Sorting them gives:

GAEDBHFD

Therefore, the next permutation after GAEDBHFC is GAEDBHFD.

The correct answer is:

b. GAEDBHFD

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Which function matches the table?

Answers

Answer:

B. f(x) =3

Step-by-step explanation:

sbwveivdebeudh

no links
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can hold a maximum of 110 people. The drama club must make at least $570 from ticket sales to cover the show's costs. Also, they must sell at least 20 student tickets and a maximum of 70 adult tickets. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

Answers

Answer:

hgfxjdt

Step-by-step explanation:

Hey I'm Chloe Can you Help Me, I will give Brainlest, Thank you :)
Stefan sells Jin a bicycle for ​$104 and a helmet for ​$17. The total cost for Jin is 110 ​% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend​ originally? How much money did he make by selling the bicycle and helmet to​ Jin?

Answers

Answer:

Stefan spent 108.9$ and made 12.1$

Step-by-step explanation:

Hey I'm Aiden I can help you, I will take Brainlest, Your welcome :)

take 10% of 121 and subtract it from 121 and you get the price he paid and made

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