Question

A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. According to the model, how many fish of the new species were released initially?

Answer 1

7 fishes

Explanation:

Given the growth of the population of fish which is modeled by the exponential function:

`P(t)=7 \cdot b^t`

Where:

t=time in weeks after release

b=growth rate of the fish

At t=0

`P(0)=7 \cdot b^0\\P_0=7 \cdot 1 \\P_0=7`

The initial number,
`P_0` of fish which was released into the lake is 7.