Respuesta :
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).
[tex]P(t)=1000e^{0.16t}[/tex]
We need to find the number of years after which population reach 4000.
Substitute P(t)=4000 in the above function.
[tex]4000=1000e^{0.16t}[/tex]
Divide both sides by 1000.
[tex]4=e^{0.16t}[/tex]
Taking ln on both sides.
[tex]\ln 4=\ln e^{0.16t}[/tex]
[tex]1.3863=0.16t[/tex] [tex][\because \ln e^x=x][/tex]
Divide both sides by 0.16.
[tex]\dfrac{1.3863}{0.16}=t[/tex]
[tex]8.664375=t[/tex]
We need to find the number of years. So, round the answer to the next whole number.
[tex]t\approx 9[/tex]
Therefore, after 9 years, the population reach 4000.
