Deternmine the multiplier. Since 2005 is the start, this will be 0. The point will be (0,60).

\(\displaystyle{y}={a}{b}^{{x}}\) Write the equation

\(\displaystyle{60}={a}{b}^{{0}}\) Substitute the values

\(60=a(1)\) Use zero rule of exponent

\(60=a\) Simplify

In order to determine b, use point (5,45) for 2010.

\(\displaystyle{y}={a}{b}^{{x}}\) Write the equation

\(\displaystyle{45}={60}{\left({b}\right)}^{{5}}\) Substitute the values

\(\displaystyle\frac{{45}}{{65}}={60}\frac{{\left({b}\right)}^{{5}}}{{60}}\) Divide both sides by 60

\(0.75=b^5\) Simplify

\(\displaystyle{5}\sqrt{{0.75}}={5}\sqrt{{b}}^{{5}}\) Use radical to remove exponent

0.944=b Simplify

The multiplier is 0.944. Subtract the multiplier from 1 to determine the percent decrease. 1-0.944=0.056= 5.6%

The exponential function for the given situation is: \(\displaystyle{f{{\left({x}\right)}}}={60}{\left({0.944}\right)}^{{x}}\)

Using the exponential function, \(\displaystyle{f{{\left({x}\right)}}}={60}{\left({0.944}\right)}^{{x}}\), determine the value in 2020, which is 15 years from 2005.

\(\displaystyle{f{{\left({x}{0}\right)}}}={60}{\left({0.944}\right)}^{{x}}\) Write the function

\(\displaystyle{f{{\left({15}\right)}}}={60}{\left({0.944}\right)}^{{15}}\) Substitute the values

\(f(15)=25.28\) Perform operation