Question

From 1980 to 2007 the number of drive-in theaters in the United States can be modeled by the function d(t) = -0.1413t³ + 9.642t² - 232.5t +2421 where d(t) is the number of open theaters and t is years after 1980.

Use a graphing calculator to graph the function over the interval 0 st s 27. Describe the behavior of the function over the interval.

Answer 1

The function d(t) = -0.1413t³ + 9.642t² - 232.5t + 2421 models the number of drive-in theaters in the United States from 1980 to 2007. Graphing the function over the interval 0 ≤ t ≤ 27 will show the trend of the number of open theaters over time.

Step-by-step explanation:

The given function that models the number of drive-in theaters in the United States from 1980 to 2007 is:

d(t) = -0.1413t³ + 9.642t² - 232.5t + 2421

To graph the function over the interval 0 ≤ t ≤ 27, we can use a graphing calculator. The graph will show the behavior of the function over time, representing the number of open theaters.

From the graph, we can observe the trend of the number of drive-in theaters as time increases. The behavior may include fluctuations, turning points, and overall increase or decrease.