Question

A study is done on the population of a certain fish species in a lakeSuppose that the population size P(s) after years is given by the following exponential function P(t) = 550 * (138) ^ t

Answer 1

Given the exponential function:

`P(t)=550(1.38)^t`

We can rewrite this equation as follows:

`P(t)=550(1+0.38)^t=550(1+(38)/(100))^t...(1)`

For the initial population size, we evaluate the function for t = 0:

`\begin{gathered} P(0)=550(1+(38)/(100))^0=550(1) \\ \\ \therefore P(0)=550 \end{gathered}`

The initial population size is 550.

Looking at (1), the growth rate is 0.38. Since this is a positive value, this function represents growth.

`0.38=(38)/(100)=38\%`

The population size changes by 38% each year.