1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kvv77 [185]
3 years ago
9

In a research lab, a cell biologist is growing a strain of bacteria under two different conditions. Culture A had an initial pop

ulation of 200 and doubles every hour. Culture B had an initial population of 819200 but has been contaminated. Its population is now decreasing by half every hour. When will the two cultures have an equivalent population? Solve using an exponential equation.
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
3 0

Answer:

They will have the same population after 6 hours

Step-by-step explanation:

The general exponential equation format for this is;

P = P_o(e^(kt))

For Culture A, we are told that it had an initial population of 200 and doubles every hour.

Thus;

After 1 hour, P = 400

After 2 hours, P = 800

After 3 hours, P = 1600

Thus;

At t = 1, we have;

400 = 200(e^(k × 1))

400/200 = e^(k)

e^(k) = 2 - - - (eq 1)

At t = 2, we have;

800 = 200(e^(k × 2))

800/200 = e^(2k)

e^(2k) = 4 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 4/2

e^(2k - k) = 2

e^(k) = 2

k = In 2

k = 0.6931

Thus;

P = 200e^(0.6931t)

For Culture B, we are told that it had an initial population of 819200 but has been contaminated. Its population is now decreasing by half every hour.

Thus;

After 1 hour, P = 409600

After 2 hours, P = 204800

After 3 hours, P = 102400

Thus;

At t = 1, we have;

409600 = 819200(e^(k × 1))

409600/819200 = e^(k)

e^(k) = 0.5 - - - (eq 1)

At t = 2, we have;

204800 = 819200(e^(k × 2))

204800/819200 = e^(2k)

e^(2k) = 0.25 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 0.25/0.5

e^(k) = 0.5

k = In 0.5

k = -0.6931

Thus;

P = 819200(e^(-0.6931t))

We want to find the time when the 2 cultures will have the same population. Thus;

200e^(0.6931t) = 819200(e^(-0.6931t))

Arranging, we have;

(e^(0.6931t))/(e^(-0.6931t)) = 819200/200

e^(0.6931t - (-0.6931t) = 4096

e^(1.3862t) = 4096

1.3862t = In 4096

1.3862t = 8.3178

t = 8.3178/1.3862

t ≈ 6 hours

You might be interested in
2 Describe the solution set of y=8
Vedmedyk [2.9K]

Answer:

what is your question there is no equation

7 0
2 years ago
Janelle earned 90% on a test and got 63 points. How many total points were possible on the test?
aliina [53]

Answer:

70

Step-by-step explanation:

8 0
3 years ago
a deer tick measures 29 centimeters in length in a photograph. if the photo has been enlarged by a factor of 100, what is the ac
N76 [4]
.29 cm in length

29 ÷ 100 = .29
3 0
3 years ago
Danny reads for one half hour every day.
fgiga [73]

There are 7 days in a week.

1/2 hour x 7 days = 3 1/2 hours per week.

3 1/2 hours per week x 4 weeks = 14 hours

He read for a total of 14 hours

8 0
3 years ago
Read 2 more answers
The lifetime of a certain brand of battery is known to have a standard deviation of 9 hours. Suppose that a random sample of 150
Kobotan [32]

Answer:

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.05 = 0.95, so Z = 1.645.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.645\frac{9}{\sqrt{150}} = 1.2

The lower end of the interval is the sample mean subtracted by M. So it is 40.5 - 1.2 = 39.3 hours

The upper end of the interval is the sample mean added to M. So it is 40.5 + 1.2 = 41.7 hours

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

7 0
2 years ago
Other questions:
  • Which example illustrates the distributive property? 4 + 5 = 5 + 4 3(x + 4) = 3x + 12 5 * 1 = 5 4 + (5 + 6) = (4 + 5) + 6
    11·2 answers
  • Catherine walks her dog 3/4 mile everyday. how far does she walk each day?
    6·2 answers
  • HELP ME FOR POINTS AND BRAINETEST
    7·2 answers
  • 0.75 is 10 times as much as
    11·2 answers
  • Negation "If it rains then I take an umbrella."
    9·1 answer
  • A real estate agent earns about a 6% commission on each house sold. How
    14·2 answers
  • Wade has $475 in a savings account at the
    6·1 answer
  • I need help on this question thanks
    12·1 answer
  • Identify the center and radius of each. Then sketch the graph.<br> (x-1) +(v + 3) = 4
    7·1 answer
  • 13.62<br><br> Round to the<br> nearest whole<br> number.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!