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

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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(13209) About Me  (Show Source):
You can put this solution on YOUR website!


P%28t%29+=+%28200%2B40t%29%2F%281%2B0.05t%29

graph%28400%2C400%2C-4%2C24%2C-50%2C600%2C%28200%2B40x%29%2F%281%2B0.05x%29%2C500%29

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

%28200%2B40t%29%2F%281%2B0.05t%29=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)).

%28P%2812%29-P%284%29%29%2F%2812-4%29

Both parts of the problem can be worked with pencil and paper; but a graphing calculator makes it much easier....