SOLUTION: ``The size P of a certain insect population at time t​ (in days) obeys the function P(t)=700e^0.05t ​(a) Determine the number of insects at t=0 days. ​(b) W

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Question 1088640: ``The size P of a certain insect population at time t​ (in days) obeys the function P(t)=700e^0.05t
​(a) Determine the number of insects at t=0 days.
​(b) What is the growth rate of the insect​ population?
​(c) What is the population after 10​ days?
​(d) When will the insect population reach 1050?
​(e) When will the insect population​ double?

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
P(0)=700e^0=700.
growth rate is 0.05 or 5%
after 10 days 700*e^0.5
1154.10 or 1154 after 10 days.
=======================
1050=700e^(0.05t)
divide by 700
1.5=e^0.05t
ln both sides
ln 1.5=0.05 t
8.11 days.
=======================
doubling time crudely is rule of 72, where 72/5 is about 14.
1400=700e^0.05t
2=e^0.05t
ln2=0.05t
13.86 years.

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