Question

A bank deposit yields $802.50 in interest every year. How many years will it take to yield 6.42×104
dollars? Write the answer in scientific notation.(1 point)
Responses

8×101
8 times 10 superscript 1 baseline

8×104
8 times 10 superscript 4 baseline

1.25×102
1.25 times 10 squared

8×102

Answer 1

To find out how many years it will take for the bank deposit to yield \( 6.42 \times 10^4 \) dollars in interest at a rate of $802.50 per year, we can use the formula:

\[
\text{Number of years} = \frac{\text{Total interest}}{\text{Annual interest}}
\]

Substituting the numbers into the equation:

\[
\text{Number of years} = \frac{6.42 \times 10^4}{802.50}
\]

First, we calculate the division:

\[
\frac{6.42 \times 10^4}{802.50} \approx \frac{64200}{802.50} \approx 80
\]

This means it will take approximately 80 years. In scientific notation, \( 80 \) can be represented as:

\[
8.0 \times 10^1
\]

The closest response that is equivalent to this value is \( 8 \times 10^1 \).

Therefore, the answer is:

**8×10¹.**