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 to the 1th power - no response given

1.25×102
1 point 2 5 times 10 squared - no response given

8×102
8 times 10 raised to the 2 power - incorrect

8×104

Answer 1

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

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

Plugging in the values, 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:

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

Now, let's perform the division:

\[
\text{Number of Years} = \frac{6.42 \times 10^4}{802.50} \approx 80
\]

Expressing \(80\) in scientific notation gives us:

\[
80 = 8.0 \times 10^1
\]

Therefore, the answer in scientific notation is:

\[
\boxed{8 \times 10^1}
\]