Question

A fisherman illegally introduces some fish into a lake, and they quickly propagate. The growth of the population of this new species (within a period of a few years) is modeled by P(x)=7b^x

, where x is the time in weeks following the introduction and b is a positive unknown base.



a. Exactly how many fish did the fisherman release into the lake?

Answer 1

To determine how many fish the fisherman released into the lake, we need another piece of information that relates to the population of the new species at a certain time. Let's say that after 5 weeks, the population of the new species has grown to 500 fish. Then we can set up an equation:

P(5) = 7b^5 = 500

Solving for b, we get:

b^5 = 500/7

b = (500/7)^(1/5)

b ≈ 1.828

Now we can find the initial population P(0):

P(0) = 7b^0 = 7(1) = 7

Therefore, the fisherman illegally introduced 7 fish into the lake.