Question

The number of members in the hiking club was 23 in 2000 and has increased by 18% each year. Which model shows the club's membership in terms of t, the number of years since 2000?

Answer 1

Step-by-step explanation

We are asked to get the option that models the club's membership in terms of t

To find the answer, we need to be aware that this is a growth function because the number of members increases

Thus

`P=P_o(1+r)^n`

In our case

`\begin{gathered} P_0=23 \\ r=18\text{ \% =0.18} \\ n=t \end{gathered}`

So putting all the terms together, we will have

`\begin{gathered} y=23(1+0.18)^t \\ \\ y=23(1.18)^t \end{gathered}`

Where t is the number of years after 2000

The answer is

`y=23(1.18)^t`