Respuesta :
Answer:
The exponential function that satisfies the given conditions is [tex]P(t)=30(1.13)^t[/tex].
Step-by-step explanation:
If a population [tex]P[/tex] is changing at a constant percentage rate [tex]r[/tex] each year, then
[tex]P(t)=P_0(1+r)^t[/tex]
where [tex]P_0[/tex] is the initial value, [tex]r[/tex] is expressed as a decimal, and [tex]t[/tex] is time in years.
This function is known as an exponential growth function.
We know that the initial value is 30 and it is increasing at a rate of 13% per year. Therefore, using the above definition we get that,
[tex]P_0=30\\r=0.13[/tex]
[tex]P(t)=30(1+0.13)^t=30(1.13)^t[/tex]
