The number of drive-in movie theaters in the United States from 1995 to 2018 can be modeled by the function $d(t)=-0.086t^3+3.71t^2-53.7t+643$ where $t$ is the number of years after 1995.

a. Use technology to identify the graph of the function for $1\le t\le23$ .

Responses

Graph of a curve on a coordinate plane. The curve begins at ordered pair 1 comma 450, passes through the ordered pairs 4 comma 550, 8 comma 600 and ends at ordered pair 14 comma 610.

• image with description: Graph of a curve on a coordinate plane. The curve begins at ordered pair 1 comma 450, passes through the ordered pairs 4 comma 550, 8 comma 600 and ends at ordered pair 14 comma 610. - - no response given

Graph of a curve on a coordinate plane. The curve begins at ordered pair 1 comma 600, passes through the ordered pairs 8 comma 400, 12 comma 390 and ends at ordered pair 22 comma 340.

• image with description: Graph of a curve on a coordinate plane. The curve begins at ordered pair 1 comma 600, passes through the ordered pairs 8 comma 400, 12 comma 390 and ends at ordered pair 22 comma 340. - - correct

Graph of a curve on a coordinate plane. The curve begins at ordered pair 0 comma 200, passes through the ordered pairs 8 comma 400, 12 comma 400 and ends at ordered pair 16 comma 400.

• image with description: Graph of a curve on a coordinate plane. The curve begins at ordered pair 0 comma 200, passes through the ordered pairs 8 comma 400, 12 comma 400 and ends at ordered pair 16 comma 400. - - no response given

Graph of a curve on a coordinate plane. The curve begins at ordered pair 2 comma 800, passes through the ordered pairs 8 comma 800, 12 comma 400 and ends at ordered pair 16 comma 200.

• image with description: Graph of a curve on a coordinate plane. The curve begins at ordered pair 2 comma 800, passes through the ordered pairs 8 comma 800, 12 comma 400 and ends at ordered pair 16 comma 200. - - no response given Question 2 Describe the behavior of the graph on this interval. 0 / 10000 Word Limit Question 3 b. Find and interpret the average rates of change in the number of drive-in movie theaters from 1996 to 2006 and from 2006 to 2018. Round your answers to the nearest whole number. From 1996 to 2006 the average rate of change is about theaters per year.

From 2006 to 2018 the average rate of change is about theaters per year.

Question 4 c. Do you think this model can be used for years before 1995 or after 2018? Responses

Yes Yes - no response given

No No - correct Question 5 Explain. 0 / 10000 Word Limit Skip to navigation