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 point 2 5 times 10 squared

8×104
8 times 10 to the 4th power

8×101
8 times 10 to the 1th power

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, we can use the formula:

\[
\text{Years} = \frac{\text{Total Interest}}{\text{Interest per Year}}
\]

In this case:

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

Now we can calculate the number of years:

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

Calculating the division:

1. First, we can convert \( 802.50 \) into scientific notation:
\( 802.50 = 8.025 \times 10^2 \)

2. Now, we can perform the division:

\[
\text{Years} = \frac{6.42 \times 10^4}{8.025 \times 10^2}
\]

3. Dividing the coefficients and subtracting the exponents gives:

\[
\text{Years} = \frac{6.42}{8.025} \times 10^{4-2} \approx 0.800 \times 10^2
\]

4. Converting \( 0.800 \) into proper scientific notation gives:

\[
\text{Years} \approx 8.00 \times 10^1
\]

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

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