Chapter 6.1, Problem 62E

To determine

To write: an equation that represents the function.

Answer to Problem 62E

  $g(x)=5{(2)}^x.$

Explanation of Solution

Given information: A function g models a relationship in which the dependent variable is multiplied by $4$ for every $2$ units the independent variable increases. The value of the function at $0$ is $5$ .

Calculation:

Make a table values:

x	0	2	4	6
y	5	20	80	320

The y − intercept is 5.

From the table, the y − values increase by a factor of 4 as x increases by 2.

The model will be:

  $\begin{array}{}$ y=5{(4)}^{x/2}$$ y=5{\left(4^{12}\right)}^x$$ y=5{(\sqrt{4})}^x$$ y=5{(2)}^x$$ g(x)=5{(2)}^x$\end{array}$