Yearly attendance at a local movie theater is 56,000 and grows continuously at a rate of 4.2% each year. What is the approximate attendance at the movie theater in nine years?

Yearly attendance = 56,000

The growth rate is 4.2% or 0.042 per year.

That is,

Year 0: 56,000

Year 1: 56,000*1.042

Year 2: 56,000*1.042²

and so on.

This is a geometric sequence with

a₁ = 56,000 and r = 1.042

The n-th term is

a (n) = a₁ rⁿ⁻¹

When n=9, obain

a₉ = 56,000*1.042⁸ = 77,826.9 ≈ 77,827

Answer: 77,827