Chapter 7.7, Problem 15PPS

To determine

To construct an exponential function to model the given graph.

Answer to Problem 15PPS

  $y=5{\left(2\right)}^x$

Explanation of Solution

Given:

Graph passes through the points (1, 10) and (5, 160).

Calculation:

Given curve passes through the points (1, 10) and (5, 160).

Let the required exponential function be

  $y=a\cdot b^x$

Now put (1, 10) in $y=a\cdot b^x$ , we get

  $\begin{array}{l}10=a\cdot b^1\\ \Rightarrow a\cdot b=10\to \left(1\right)\end{array}$

Now put (5, 160) in $y=a\cdot b^x$ , we get

  $\begin{array}{l}160=a\cdot b^5\\ \Rightarrow a\cdot b^5=160\to \left(2\right)\end{array}$

Now dividing equation (2) by equation (1), we get

  $\begin{array}{l}\frac{a\cdot b^5}{a\cdot b}=\frac{160}{10}\\ \Rightarrow b^4=16\\ \Rightarrow b=2\end{array}$

Now put $b=2$ in equation (1), we get

  $\begin{array}{l}a\cdot 2=10\\ \Rightarrow a=5\end{array}$

Hence the required exponential function is,

  $y=5{\left(2\right)}^x$