Respuesta :
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:
[tex]a\cdot(1+r)^n[/tex]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,
[tex]m=550\cdot(1+\frac{3}{100})^t[/tex]This way, for 2020 the gym would have
[tex]\begin{gathered} m=550\cdot(1+\frac{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}[/tex]Around 964 memberships sold
