Question

The size P of a small herbivore population at time t (in years) obeys the function P(t) = 1000e0-16t if they have enough food and the predator population stays constant. After how many years will the population reach 4000?

Answer 1

Answer:

After 9 years, the population reach 4000.

Step-by-step explanation:

The given function P(t) represents the size of a small herbivore population at time t (in years).

$P(t)=1000e^{0.16t}$

We need to find the number of years after which population reach 4000.

Substitute P(t)=4000 in the above function.

$4000=1000e^{0.16t}$

Divide both sides by 1000.

$4=e^{0.16t}$

Taking ln on both sides.

$\ln 4=\ln e^{0.16t}$

$1.3863=0.16t$                 $[\because \ln e^x=x]$

Divide both sides by 0.16.

$\dfrac{1.3863}{0.16}=t$

$8.664375=t$

We need to find the number of years. So, round the answer to the next whole number.

$t\approx 9$

Therefore, after 9 years, the population reach 4000.