Question

The function f(t) = 750t + 20,000 models the number of movie theaters in the United States t years after 1985. Use this equation to predict the year in which the United States will have 35,000 movie theaters.

Answer 1

Given:

The function models the number of movie theaters in the United States t years after 1985.

$f(t)=750t+20,000$

To find:

The year in which the United States will have 35,000 movie theaters.

Solution:

We have,

$f(t)=750t+20,000$

Putting f(t)=35000, we get

$35,000=750t+20,000$

$35,000-20,000=750t$

$15,000=750t$

Divide both sides by 750.

$\dfrac{15,000}{750}=t$

$20=t$

It means, United States will have 35,000 movie theaters 20 years after 1985.

$1985+20=2005$

Therefore, United States will have 35,000 movie theaters is 2005.