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

1.25×102
1.25 times 10 squared

8×102
8 times 10 squared

8×104

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 when it yields $802.50 in interest every year, we can set up the equation:

\[
\text{Total Interest} = \text{Interest per Year} \times \text{Number of Years}
\]

In this case, we have:

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

To find the number of years, we can rearrange the equation:

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

Calculating this gives:

\[
\text{Number of Years} = \frac{6.42 \times 10^4}{802.50} \approx 80.0
\]

To express \( 80.0 \) in scientific notation:

\[
80.0 = 8.0 \times 10^1
\]

Thus, the answer in scientific notation is:

**\( 8 \times 10^1 \)**.