Chapter 9.2, Problem 83E

To determine

To find: The total sales during the first 10 years of this business, and to find what type of economic factors could prevent the business from meeting its goals.

Answer to Problem 83E

Total sales in 10 years are $375000.

The economic factors that could prevent the business form meeting goals are,

1. Income
2. Inflation
3. Interest Rate
4. Recession
5. Exchange Rate

Explanation of Solution

Given information:

As entrepreneur sells $15000 worth of sports memorabilia during one year and sets a goal increasing annual sales by $5000 each year for the next 9 years. Assuming that the entrepreneur meets this goal.

Calculation:

Total sales during the 10 years of business can be calculated by knowing the amount in the ${10}^{th}$ year by substituting $n=10$ in $a_n=a_1+\left(n-1\right)d$ with $a_1=15000,d=5000$ ,

  $\begin{array}{c}{a}_{10}=15000+\left(10-1\right)\left(5000\right)\\ =15000+9\left(5000\right)\\ =60000\end{array}$

The total sales can be calculated by using the partial sum formula,

  $S_n=\frac{n}{2}\left(a_1+a_{10}\right)$

Substitute $n=10,a_1=15000,a_{10}=60000$ in the above formula, $n=10,a_1=15000,a_{10}=60000$

  $\begin{array}{c}{S}_n=\frac{10}{2}\left(15000+60000\right)\\ =5\left(75000\right)\\ =375000\end{array}$

Hence, total sales in 10 years are $375000.

The economic factors that could prevent the business form meeting goals are,

6.Income

7.Inflation

8.Interest Rate

9.Recession

10.Exchange Rate