Given the exponential function:
[tex]P(t)=550(1.38)^t[/tex]
We can rewrite this equation as follows:
[tex]P(t)=550(1+0.38)^t=550(1+\frac{38}{100})^t...(1)[/tex]
For the initial population size, we evaluate the function for t = 0:
[tex]\begin{gathered} P(0)=550(1+\frac{38}{100})^0=550(1) \\ \\ \therefore P(0)=550 \end{gathered}[/tex]
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.
[tex]0.38=\frac{38}{100}=38\%[/tex]
The population size changes by 38% each year.
