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 your answer in scientific notation.
A. 8×10^3
B. 1.25×10^2
C. 8×10^2
D. 8×10^4
A. 8×10^3
B. 1.25×10^2
C. 8×10^2
D. 8×10^4
Answers
GPT-4o mini
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.
\[
\text{Total Interest} = \text{Annual Interest} \times \text{Number of Years}
\]
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.