13.2k views
2 votes
How do you do the last two questions?

How do you do the last two questions?-example-1
How do you do the last two questions?-example-1
How do you do the last two questions?-example-2
How do you do the last two questions?-example-3

1 Answer

5 votes

Answer:

P = 6200 / (1 + 5.2e^(0.0013t))

increases the fastest

Explanation:

dP/dt = 0.0013 P (1 − P/6200)

Separate the variables.

dP / [P (1 − P/6200)] = 0.0013 dt

Multiply the left side by 6200 / 6200.

6200 dP / [P (6200 − P)] = 0.0013 dt

Factor P from the denominator.

6200 dP / [P² (6200/P − 1)] = 0.0013 dt

(6200/P²) dP / (6200/P − 1) = 0.0013 dt

Integrate.

ln│6200/P − 1│= 0.0013t + C

Solve for P.

6200/P − 1 = Ce^(0.0013t)

6200/P = 1 + Ce^(0.0013t)

P = 6200 / (1 + Ce^(0.0013t))

At t = 0, P = 1000.

1000 = 6200 / (1 + C)

1 + C = 6.2

C = 5.2

P = 6200 / (1 + 5.2e^(0.0013t))

You need to change the exponent from negative to positive.

The inflection points are where the population increases the fastest.

User Lewis Kelsey
by
6.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.