Chapter 0.3, Problem 65E

Diabetes Using data from $2010$ and projected to $2050$, the number of millions of U.S. adults with diabetes, $y$, can be approximated by the formula

$y=\frac{120}{1+5.25{\left(1.066\right)}^{-t}}$ where $t$ is the number of years after $2000$

(Source: Centers for Disease Control and Prevention).

The actual numbers of millions given by the CDC for selected years are as follows.

$\begin{array}{ccc}2010& 2015& 2020\\ 32.3& 37.3& 50.0\end{array}$

For each of these years, find he number of U.S. adults with diabetes predicted by the formula. Round your answer to one decimal place.

Using the number of U.S. adults with diabetes given above for $2015$, how many more U.S. adults with diabetes does the formula predict will be added by $2025$?

Why is it reasonable that the formula approximating the number of U.S. adults with diabetes has an upper limit that cannot be exceeded? Use large $t$

-values to discover this formula's upper limit.