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((320)/(200))=0.08t`
`(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((400)/(200))=0.08t`

t=8.664

then the population will double in 8.66 years