SOLUTION: Suppose that 200 fish are introduced into a protected lake. The fish population can be approximated by P=200+40t over 1+0.05t , with t being the time in years since the fish were

Question 1143282: Suppose that 200 fish are introduced into a protected lake. The fish population can be approximated by P=200+40t over 1+0.05t , with t being the time in years since the fish were introduced into the lake.
a. Determine the time needed for the fish population to reach 500.
b. Determine the average rate of change of the fish population with respect to time from 4 years until 12 years since the fish were introduced into the lake.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

1. Time for the population to reach 500: Solve the equation P(t) = 500

2. Average rate of change of the population from year 4 to year 12: That's the slope of the line passing through (4,P(4)) and (12,P(12)).

Both parts of the problem can be worked with pencil and paper; but a graphing calculator makes it much easier....
RELATED QUESTIONS
Suppose that 40 deer are introduced in a protected wilderness area. The population of... (answered by solver91311)

Suppose that 40 deer are introduced in a protected wilderness area. The population of the (answered by ikleyn)

Recursive equations can be very handy for modeling complicated situations for which... (answered by ikleyn)

An initial population of 30 fish is introduced into a lake. This fish population grows... (answered by Theo,ikleyn)

An initial population of 280 fish is introduced into a lake. This fish population grows... (answered by josgarithmetic)

there are two types of fish in the lake. fish type A has a current population of 5750... (answered by stanbon)

Can someone please assist me in setting this equation up and explain why I am doing it in (answered by ankor@dixie-net.com)

The fish population of a lake is modeled by the function P=(10)/(1+4e^(-0.8t))... (answered by josmiceli)

A large pond is stocked with fish.The fish population P is modeled by the... (answered by ankor@dixie-net.com)