Question

= Homework: 6.8Question 1, 6.8.1Part 1 of 5The size P of a certain insect population at time t (in days) obeys the function P(t) = 200 e0.)(a) Determine the number of insects at t = 1 days0.087e

Answer 1

Given the function

$P(t)=200e^{0.08t}$

A)t=0

$P(0)=200e^0$$P(0)=200$

Then the population of insects in t=0 is 200

B)

rate=0.08

C) population after 10 years t=10

$P(10)=200e^{0.08*10}$$P(10)=445.108$

then in 10 years the population will be 445.11

D)when will the population reach 320 P(t)=320

$320=200e^{0.08t}$

Solve for t

$ln(\frac{320}{200})=0.08t$$\frac{0.47}{0.08}=t$

t=5.875

then

the population will reach 320 after 5.88 years

e) when will the insect population double p(t)=400

$400=200e^{0.08t}$$ln(\frac{400}{200})=0.08t$

t=8.664

then the population will double in 8.66 years