Question

The yearly attendance at a local movie theater is 68,000 and grows continuously at a rate of 3.5% each year what is the approximate attendance at the movie theatre in eight years

Answer 1

`3.5 * 8 - 68000`
the answer is 67972

Answer 2

Answer: 89973

Explanation:

The exponential growth equation for growth continuously with rate r in time t is given by :-

`y=Ae^(rt)`, where A is the initial amount .

Given : The yearly attendance at a local movie theater is 68,000 and grows continuously at a rate of 3.5% each year,.

i.e. r=3.5%=0.035

A= 68,000

Then function of growth in yearly attendance will be :-

`y=68000e^(0.035t)`

At t= 8 , we have

`y=68000e^(0.035*8)=68000e^(0.28)\\\\=68000*1.32312981234\\\\=89972.8272391\approx89973`

Hence, the approximate attendance at the movie theater in eight year =89973