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
Alexandra [31]
3 years ago
13

A bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. After 6 hours there will be 3960 bacte

ria. (a) Express the population after t hours as a function of t. population: (function of t) (b) What will be the population after 3 hours?
Mathematics
1 answer:
scoray [572]3 years ago
4 0

Answer:

a) P(t) = 660 e^{\frac{ln(6)}{6} t}

b) P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617

Step-by-step explanation:

For this case we have the following info:

P(0) = 660 represent the initial amount of bacteria

P(6) = 3960 represent the population of bacteria after 6 hours

Part a

For this case we use the proportional model given by:

\frac{dP}{dt}= kP

Where P represent the population at time t and k is a constant of proportionality.

We can rewrite the model like this:

\frac{dP}{P} = k dt

And if we integrate both sides we got:

ln |P|= kt + C

Now if we apply exponential we got:

P = e^{kt +c}= e^{kt} e^C

P(t)= P_o e^{kt}

For this case using the initial condition:

660 = P_o e^{0k}, P_o = 660

We have the following model:

P(t) = 660 e^{kt}

Using the second condition P(6) = 3960 we have this:

3960 = 660e^{6k}

We can divide both sides by 660 and we got:

6= e^{6k}

Now we can apply natural log on both sides and we got:

ln (6)= 6k

k = \frac{ln(6)}{6}=0.2986265782

So then the model would be given by:

P(t) = 660 e^{\frac{ln(6)}{6} t}

Part b

For this case we just need to replace t=3 into the model and we got:

P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617

You might be interested in
Somebody please help 9 through 16
MissTica
Try to find the best domnatior and then do the mixed number then simplify
8 0
3 years ago
Will give brainlst <br> Have a nice day
Zarrin [17]

Answer:

ok where are you from which country

5 0
2 years ago
How would you figure this out?
Anit [1.1K]

the 10 ounce drink is a better deal. it costs less per ounce.

5 0
3 years ago
How do you find the total sum of squared values?
tester [92]

Answer:

Step-by-step explanation:

\sum^{12}_{r=1} r^2 = \frac{12(12+1)(2*12+1)}{6}= A

\sum_{r=3}^{12}= \sum_{r=1}^{12} - (r_1+r_2)

r_1= 1^2

r_2= 2^2

you do your math!!

7 0
3 years ago
What is the solution to x in 3(x+2)-4x+2=3x+2(x-8)
NeTakaya

Answer:

x=4

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • How many miles did I run
    15·2 answers
  • The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. what is the probability that
    7·1 answer
  • older car weighs 2 tons. A newer model of the car weighs 40 pounds more than the previous model. How much does the newer model o
    15·2 answers
  • A 20 foot extension ladder liens against a building if the base of the latter is placed 6 feet from the base of the building wha
    14·1 answer
  • A housewife deposited Rs 10,000 on saving account at 5% p.a. interest compounded
    12·1 answer
  • HELP ASAP, LINKS AND ABSURD ANSWERS WILL BE REPORTED! I WILL MARK BRAINLIEST!!
    6·1 answer
  • On a standardized aptitude test, scores are normally distributed with a mean of 100 and a standard deviation of 10. Find the per
    8·1 answer
  • When a figure is rotated, does every point move the same distance? Explain.
    5·1 answer
  • -1/a^-2 pls help lols
    9·1 answer
  • The graph below shows the solution set of a certain inequality. State one solution represented by the graph.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!