Question

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

Answer 1

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,

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

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