Chapter ISG, Problem 7.5.2P

a.

To determine

Whether the equation that models the scatter plot shows the projected student enrollment at East Hills High School over the next ten years can be modeled by the equation $y=1300{(1.03)}^x$ .

Answer to Problem 7.5.2P

No not agree.

The equation of the projected enrollment students will be :

  $y=1300{(1.03)}^{-x}$ (A continues decay exponential function)

Explanation of Solution

Given information: The scatter plot shows the projected student enrollment at East Hills High School over the next ten years is shown below.

  

B believes the projected enrollment at East Hills High School can be modeled by the equation $y=1300{(1.03)}^x$ .

Calculation:

No not agree because $y=1300{(1.03)}^x$ is a continues growth exponential function and scatter plot shows continues decay exponential function since number of student enrolled decreases as years increases.

Therefore, the equation of the projected enrollment students will be :

  $y=1300{(1.03)}^{-x}$ (A continues decay exponential function)

b.

To determine

To estimate: the projected enrollment 8 years from now using the graph.

Answer to Problem 7.5.2P

  $y_8\approx 1026.23$ .

Explanation of Solution

Given information: The equation of the projected enrollment students will be:

  $y=1300{(1.03)}^{-x}$ .

Calculation:

To estimate the projected enrollment 8 years from now putt x =8 in the function equation.

  $\begin{array}{l}$ y=1300{(1.03)}^{-x}=1300{(1.03)}^{-8}\approx 1026.23$y_8\approx 1026.23\end{array}$ .