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

8×102
8 times 10 squared

1.25×102
1.25 times 10 squared

8×101
8 times 10 superscript 1 baseline

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, we can use the formula:

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

In this case, the total interest is \( 6.42 \times 10^4 \) dollars and the annual interest is $802.50. We can set up the equation:

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

Now, we can solve for the number of years:

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

Calculating the right side:

First, divide \( 6.42 \times 10^4 \) by \( 802.50 \):

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

To express this in scientific notation, \( 80.0 \) can be written as:

\[
8.0 \times 10^1
\]

So the final answer is:

**8 × 10¹**

Thus, the response is **8×101**.