Given:
The function models the number of movie theaters in the United States t years after 1985.
[tex]f(t)=750t+20,000[/tex]
To find:
The year in which the United States will have 35,000 movie theaters.
Solution:
We have,
[tex]f(t)=750t+20,000[/tex]
Putting f(t)=35000, we get
[tex]35,000=750t+20,000[/tex]
[tex]35,000-20,000=750t[/tex]
[tex]15,000=750t[/tex]
Divide both sides by 750.
[tex]\dfrac{15,000}{750}=t[/tex]
[tex]20=t[/tex]
It means, United States will have 35,000 movie theaters 20 years after 1985.
[tex]1985+20=2005[/tex]
Therefore, United States will have 35,000 movie theaters is 2005.
