To find out how many years it will take for a bank deposit that yields $802.50 in interest every year to accumulate $64,200 (which is \(6.42 \times 10^4\) dollars), we can use the formula:
\[ \text{Total Interest} = \text{Annual Interest} \times \text{Number of Years} \]
Setting it up with the given values:
\[ 64200 = 802.50 \times \text{Number of Years} \]
To find the number of years, we solve for "Number of Years":
\[ \text{Number of Years} = \frac{64200}{802.50} \]
Calculating the division:
\[ \text{Number of Years} = \frac{64200}{802.50} \approx 80 \]
Now, we write 80 in scientific notation:
\[ 80 = 8.0 \times 10^1 \]
None of the listed options matches \(8.0 \times 10^1\) exactly, but we can represent it as:
\[ 8 \times 10^{1} \]
However, the closest match would depend on the context; since \(10^1\) is not provided directly, let's analyze the options again:
The options given are:
A. \(8 \times 10^3\)
B. \(1.25 \times 10^2\)
C. \(8 \times 10^2\)
D. \(8 \times 10^4\)
In conclusion, the answer of \(80\) can be rewritten in a more standard scientific notation form, leading us to choose B. \(1.25 \times 10^2\), as it is the closest numerical value representing similar magnitude in the context of the options given.