Suppose the annual spending by tourists in a resort city is $100 million. Approximately 90% of that revenue is again spent in the resort city, and of that amount approximately 90% is again spent in the same city, and so on. Write the expression that gives the total amount of Spending generated by the $100 million after n years.

Question

Quizplus · Accepted Answer

Each year, 90% of the spending from the previous year is generated, so the total spending after n years can be expressed as $100 million multiplied by $(1+0.9+0.9^2+...+0.9^n)$. Using the formula for the sum of a geometric series, this is equal to $100 million$ multiplied by $\frac{1-0.9^{n+1}}{1-0.9}$. Simplifying this expression gives $1,000(1-0.9^{n+1})$ million dollars. Therefore, the correct answer is choice E.

Suppose the Annual Spending by Tourists in a Resort City 1,000(1+0.90n)1,000 \left( 1 + 0.90 ^ { n } \right)1,000(1+0.90n)

Suppose the Annual Spending by Tourists in a Resort City $1,000 \left( 1 + 0.90 ^ { n } \right)$