Chapter 6.1, Problem 50E

To determine

To write: an exponential function that is represented by the given graph:

Answer to Problem 50E

  $y=8{\left(0.5\right)}^x$

Explanation of Solution

Concept used:

Exponential function:

  $y=a{b}^x$......(1)

Here, the y-values changes by a factor of b as x increases by 1 and the y intercept is a.

Using the given graph to make a table of values as shown below:

  

The graph intersects the y-axis at 8. This implies that y-intercept is 8.

Also from the table it can be observed that as x increases by 1 the y-values changes by a factor of 0.5.

So, substituting $a=8$ and $b=0.5$ in equation (1), the required exponential function is:

  $y=8{\left(0.5\right)}^x$