Chapter 9.7, Problem 19PPE

To determine

To find the best function that models the data and write its equation.

Answer to Problem 19PPE

The exponential function $y=540{\left(1.03\right)}^x$ best models the data.

Explanation of Solution

Given information:

The average monthly balance of a savings account is shown below:

  

Graph the data:

  

The graph seems to be linear or exponential.

Test for common ratio:

  $\begin{array}{c}\frac{556.2}{540}=1.03\\ \frac{572.89}{556.2}\approx 1.03\\ \frac{590.07}{572.89}\approx 1.03\\ \frac{607.77}{590.07}\approx 1.03\end{array}$

The y-values have a common ratio of $1.03$ . An exponential model fits the data.

Write an exponential model:

The exponential model is given by $y=a\cdot b^x$ .

The graph passes through $\left(0,540\right)$ .

  $\begin{array}{c}540=a\cdot b^0\\ a=540\end{array}$

Thus, $y=540\cdot b^x$ .

The graph also passes through $\left(1,556.2\right)$ .

Therefore,

  $\begin{array}{c}556.2=540{\left(b\right)}^1\\ b=1.03\end{array}$

Hence, the exponential model is given by $y=540{\left(1.03\right)}^x$ .