Chapter 4.1, Problem 23PPS

a.

To determine

To write: A linear equation for the attendance y after x years by x be the number of years since 2010.

Answer to Problem 23PPS

  $y=100,000x+700,000.$

Explanation of Solution

Given:

Zoos refer to the beginning of the lesson states that the 2014 attendance at the Columbus Zoo and Aquarium was about 1.1 million and in 2016 ,it was about 1.3 million.

Calculation:

Let x be the number of years since 2010 and y is the attendance .

So,1.1 million people in 2014 is represented by the point(4,1100000) and 1.3 million people in 2016 is represented by the point(6,1300000).

Use the formula for slope to find the slope between these two points:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}.\\ m=\frac{1300000-1100000}{6-4}=\frac{200000}{2}=100000.\end{array}$

Substitute the point(4,1100000) and the slope m =100000 into the slope-intercept form of a line and solve for b .

  $\begin{array}{l}y=mx+b.\\ 1100000=100000\times 4+b.\\ b=1100000-400000=700000.\end{array}$

Substitute the slope m =100000 and b= 700000 into the slope-intercept form of a line to write the equation.

  $y=100,000x+700,000.$

b.

To determine

To estimate: The zoo’s attendance in 2024.

Answer to Problem 23PPS

Zoo’s attendance in 2024 is 2,100,000 people .

Explanation of Solution

Given: Zoos refer to the beginning of the lesson states that the 2014 attendance at the Columbus Zoo and Aquarium was about 1.1 million and in 2016 ,it was about 1.3 million.

Calculation:

To find the attendance in 2024, substitute x =14 (since 2024 is 14 years after 2010) into the equation $y=100,000x+700,000.$ found in part (a) ,we get

  $y=100000\times 14+700000=1400000+700000=2,100,000.$

Conclusion:

Zoo’s attendance in 2024 is 2,100,000 people .