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

8×104
8 times 10 superscript 4 baseline

8×101
8 times 10 superscript 1 baseline

1.25×102
1.25 times 10 squared

8×102

Answer 1

To determine how many years it will take for the bank deposit to yield \( 6.42 \times 10^4 \) dollars in interest, we can use the formula:

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

Given:
- Interest per Year = $802.50
- Total Interest = \( 6.42 \times 10^4 \)

We can set up the equation:

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

To find the number of years, divide both sides by 802.50:

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

Now, let's calculate it:

\[
\text{Number of Years} \approx \frac{64200}{802.50} \approx 80
\]

Next, we express 80 in scientific notation:

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

Therefore, the number of years it will take for the deposit to yield \( 6.42 \times 10^4 \) dollars in interest is:

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