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

8×10^4

8×10^1

1.25×10^2

8×10^2

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:

\[
\text{Number of years} = \frac{\text{Total Interest}}{\text{Interest per year}}
\]

Given that the total interest desired is \(6.42 \times 10^4\) dollars and the interest per year is \(802.50\) dollars, we can substitute these values into the formula:

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

First, calculate \(802.50\) in scientific notation:

\[
802.50 = 8.025 \times 10^2
\]

Now we can express the number of years as:

\[
\text{Number of years} = \frac{6.42 \times 10^4}{8.025 \times 10^2}
\]

This simplifies to:

\[
\text{Number of years} = \frac{6.42}{8.025} \times \frac{10^4}{10^2}
\]

This can be further simplified to:

\[
\text{Number of years} = \frac{6.42}{8.025} \times 10^{4-2}
\]

Calculating the numerical value:

\[
\frac{6.42}{8.025} \approx 0.80
\]

Thus, we have:

\[
\text{Number of years} \approx 0.80 \times 10^2 = 8.0 \times 10^1
\]

In scientific notation, we express \(0.80\) as \(8.0\) with an appropriate exponent adjustment:

\[
\text{Number of years} = 8 \times 10^1
\]

Therefore, the answer is:

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