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

Answer: 89973

Step-by-step 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

$y=68000e^{0.035\times8}=68000e^{0.28}\\\\=68000\times1.32312981234\\\\=89972.8272391\approx89973$

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

Answer 2

$3.5 \times 8 - 68000$
the answer is 67972