Question

A car dealer sold 100 cars in his first year and plans to increase his sales by 10 percent each year for the next 5 years. How many cars will he have sold at the end of his fifth year? (1 point) 1,245 920 610 725

Answer 1

To find out how many cars the dealer will sell at the end of his fifth year, we can use the formula for calculating the future value with a constant percentage increase:

\[
\text{Future Sales} = \text{Initial Sales} \times (1 + \text{Growth Rate})^n
\]

Where:
- Initial Sales = 100 cars
- Growth Rate = 10% = 0.10
- \( n \) = number of years = 5

Now, substituting the values into the formula:

\[
\text{Future Sales} = 100 \times (1 + 0.10)^5
\]

Calculating \( (1 + 0.10)^5 \):

\[
(1.10)^5 \approx 1.61051
\]

Now plug this value back into the equation:

\[
\text{Future Sales} = 100 \times 1.61051 \approx 161.051
\]

This means after 5 years, he will sell approximately 161 cars in year 5.

To find the total sales over 5 years, we need to sum up the sales for each year:

1. Year 1: \( 100 \)
2. Year 2: \( 100 \times 1.10 = 110 \)
3. Year 3: \( 100 \times (1.10)^2 \approx 121 \)
4. Year 4: \( 100 \times (1.10)^3 \approx 133.1 \)
5. Year 5: \( 100 \times (1.10)^4 \approx 146.41 \)

Now, calculating the total:

\[
\text{Total Sales} = 100 + 110 + 121 + 133.1 + 146.41 \approx 610.51
\]

Since the options listed are rounded to the nearest whole number, we note that the total sales over the 5 years is **610**.

Therefore, the answer is:

**610**