#3)Movie tickets now average $9.75 a ticket, but are increasing 15% per year.How much will they cost 12 years from now?

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asked Nov 14, 2023 229k views

1 Answer

Jasper Kuperus · Answer 1 · 2023-11-21T18:24:58+0000

Notice the pattern below

$\begin{gathered} 9.75+15\%*9.75=9.75(1+0.15)\rightarrow first\text{ year} \\ (9.75(1+0.15))+0.15(9.75(1+0.15))=9.75(1+0.15)(1+0.15)=9.75(1+0.15)^2\rightarrow second\text{ year} \\ ... \\ \Rightarrow9.75(1+0.15)^n\rightarrow\text{ nth year} \end{gathered}$

Therefore, setting n=12,

$\Rightarrow C=9.75(1+0.15)^(12)=9.75(1.15)^(12)=52.1649...$

#3)Movie tickets now average $9.75 a ticket, but are increasing 15% per year.How much will they cost 12 years from now?

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1 Answer

Thus, after 12 years, the cost per ticket is 9.75(1.15)^12, approximately $52.165

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