Question

Since 2002 , admissions at movie theaters have been in a decline. The number of people y (in billions) who go to movie theaters each year can be estimated by the equation y= -0.025x + 1.25 where x represents the number of years since 2002

Answer 1

The answer is below

Explanation:

Find the x-intercept of this equation.

What does this x-intercept mean?

Use part (b) to comment on the limitations of using equations to model real data.

Solution:

The equation of a straight line is given by y = mx + b; where y and x are variables, m is the slope of the line (rate of change) and b is the y intercept.

Given the equation:

y= -0.025x + 1.25

a) The x intercept is the value of x when y = 0. Therefore:

0 = -0.025x + 1.25

0.025x = 1.25

x = 50

b) The x intercept x = 50 means that the theater admitted 0 number of people in the year 2052 (50 years after 2002).

c) The equation has limitations because from x > 50, we start to see that y is negative; and the number of people admitted cannot be negative.