Question

A bank deposit yields $802.50 in interest every year. How many years will it take to yield 6.42×10^4 dollars? Write the answer in scientific notation.(1 point)
Responses

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:

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

Here, the total interest is \( 6.42 \times 10^4 \) dollars, and the annual interest is \( 802.50 \) dollars. Let \( t \) be the number of years. We can set up the equation:

\[
6.42 \times 10^4 = 802.50 \times t
\]

To find \( t \), we rearrange the equation:

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

Now, we perform the division:

1. First, calculate \( 6.42 \times 10^4 \):
- This is \( 64200 \).

2. Now divide by \( 802.50 \):
\[
t = \frac{64200}{802.50} \approx 80
\]

Thus, the number of years \( t \) is approximately \( 80 \).

Now expressing \( t \) in scientific notation:

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

Therefore, the answer in scientific notation is:

\[
\boxed{8.0 \times 10^1}
\]