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 8×101 8 times 10 to the 1th power 8×104 8 times 10 to the 4th power 8×102 8 times 10 squared

1 answer

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

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

In this case, the total interest is \(6.42 \times 10^4\) dollars and the interest per year is \(802.50\) dollars. Let \(x\) be the number of years. Then we can set up the equation:

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

To find \(x\), we can rearrange the equation:

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

Now we can calculate \(x\):

\[ x \approx \frac{6.42 \times 10^4}{802.50} \approx \frac{64200}{802.50} \approx 80 \]

Next, we can express \(80\) in scientific notation:

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

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

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