Question

The workout gym sold 550 memberships in 2001. since then the number of member ship sold has increased 3% annually A. write an equation for the number of memberships sold at the workout gym t years after 2001B. if this trend continues , predict how many memberships the gym will sell in 2020 .

Answer 1

Notice that the 3% increase is calulated with the memberships sold the year before, and the memberships sold the year before had a 3% increase based on the memberships sold the year before that one, and so on.

We're looking at a compund growth, wich we can model using an exponential function.

Remember that this kind of growth can be modeled using the formula:

`a\cdot(1+r)^n`

Where:

• a, is the initial amount

,

• r, is the percentage growth (as a decimal)

,

• n, is the number of times this growth is applied

Now, using this and the data given, let:

• m, be the number of memberships sold.

,

• t ,the time elapsed from 2001, in years

This way,

`m=550\cdot(1+(3)/(100))^t`

This way, for 2020 the gym would have

`\begin{gathered} m=550\cdot(1+(3)/(100))^(19) \\ \\ \rightarrow m=550\cdot(1+0.03)^(19) \\ \rightarrow m=550\cdot(1.03)^(19) \\ \rightarrow m=550\cdot(1.7535\ldots) \\ \Rightarrow m=964.42 \end{gathered}`

Around 964 memberships sold