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
1.25×102
1.25 times 10 squared
8×102
8 times 10 squared
8×101
8 times 10 superscript 1 baseline
8×104
dollars? Write the answer in scientific notation.(1 point)
Responses
1.25×102
1.25 times 10 squared
8×102
8 times 10 squared
8×101
8 times 10 superscript 1 baseline
8×104
Answers
GPT-4o mini
To find out how many years it will take to yield \( 6.42 \times 10^4 \) dollars in interest with an annual interest of $802.50, we can set up the following equation:
\[
\text{Years} = \frac{\text{Total Interest}}{\text{Annual Interest}} = \frac{6.42 \times 10^4}{802.50}
\]
Calculating the division:
\[
\frac{6.42 \times 10^4}{802.50} = \frac{64200}{802.50} \approx 80
\]
Thus, the total number of years it will take is approximately 80 years.
In scientific notation, 80 can be expressed as:
\[
8.0 \times 10^1
\]
So, the correct response is:
**8×101 (8 times 10 superscript 1 baseline)**.
\[
\text{Years} = \frac{\text{Total Interest}}{\text{Annual Interest}} = \frac{6.42 \times 10^4}{802.50}
\]
Calculating the division:
\[
\frac{6.42 \times 10^4}{802.50} = \frac{64200}{802.50} \approx 80
\]
Thus, the total number of years it will take is approximately 80 years.
In scientific notation, 80 can be expressed as:
\[
8.0 \times 10^1
\]
So, the correct response is:
**8×101 (8 times 10 superscript 1 baseline)**.