Chapter 7.7, Problem 16PPS

To determine

To write: the exponential model to the graph that passes through the given two points.

Answer to Problem 16PPS

The exponential model is $y=\left(\frac{1}{8}\right)8^x$

Explanation of Solution

Given information:

Consider the exponential graph passing through the points $(1,1),(4,64)$ .

Calculation:

The exponential model is

  $\begin{array}{l}y=a{b}^x\\ (1,1)\Rightarrow 1=a{b}^1\mathrm{.....}(1)\\ (4,64)\Rightarrow 64=a{b}^4\mathrm{....}(2)\\ \frac{(2)}{(1)}\Rightarrow \frac{a{b}^4}{ab}=\frac{64}{1}\\ b^2=64\\ b=8\\ \Rightarrow a=1/8\end{array}$

Then, $y=\left(\frac{1}{8}\right)8^x$

Hence, the exponential model $y=\left(\frac{1}{8}\right)8^x$