Answer: 89973
Step-by-step explanation:
The exponential growth equation for growth continuously with rate r in time t is given by :-
[tex]y=Ae^{rt}[/tex], 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 :-
[tex]y=68000e^{0.035t}[/tex]
At t= 8 , we have
[tex]y=68000e^{0.035\times8}=68000e^{0.28}\\\\=68000\times1.32312981234\\\\=89972.8272391\approx89973[/tex]
Hence, the approximate attendance at the movie theater in eight year =89973
