Question

A bank deposit yields $802.50 in interest every year. How many years will it take to yield 6.42×104%0D%0A6.42%0D%0A×%0D%0A10%0D%0A4%0D%0A dollars? Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A8×101%0D%0A8%0D%0A×%0D%0A10%0D%0A1%0D%0A8 times 10 to the 1th power%0D%0A%0D%0A1.25×102%0D%0A1.25%0D%0A×%0D%0A10%0D%0A2%0D%0A1 point 2 5 times 10 squared%0D%0A%0D%0A8×104%0D%0A8%0D%0A×%0D%0A10%0D%0A4%0D%0A8 times 10 to the 4th power%0D%0A%0D%0A8×102

Answer 1

To determine how many years it will take for a bank deposit that yields $802.50 in interest every year to yield $64,200 (which is \(6.42 \times 10^4\) dollars), we can set up the equation:

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

Plugging in the values, we have:

\[ 802.50 \times t = 64200 \]

Where \(t\) is the number of years. To solve for \(t\), we divide both sides by 802.50:

\[ t = \frac{64200}{802.50} \]

Now, calculating this:

\[ t \approx 80 \]

To express this in scientific notation, we rewrite 80:

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

Thus, the answer in scientific notation is:

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