Question
a bank deposit yields $802.50 in interest every year. How many years will it take to yield 6.42×10 to the fourth power dollars right in scientific notation
Answers
GPT-4o mini
To find out how many years it will take to yield \( 6.42 \times 10^4 \) dollars in interest when the bank deposit yields \( 802.50 \) dollars in interest every year, you can set up the following equation:
\[
\text{Total Interest} = \text{Interest per Year} \times \text{Number of Years}
\]
Substituting the values:
\[
6.42 \times 10^4 = 802.50 \times t
\]
Where \( t \) is the number of years. Now, solve for \( t \):
\[
t = \frac{6.42 \times 10^4}{802.50}
\]
Calculating the right side:
1. Calculate \( 6.42 \times 10^4 \):
\[
6.42 \times 10^4 = 64200
\]
2. Now divide by \( 802.50 \):
\[
t = \frac{64200}{802.50} \approx 80
\]
Thus, it will take approximately **80 years** to yield \( 6.42 \times 10^4 \) dollars in interest.
\[
\text{Total Interest} = \text{Interest per Year} \times \text{Number of Years}
\]
Substituting the values:
\[
6.42 \times 10^4 = 802.50 \times t
\]
Where \( t \) is the number of years. Now, solve for \( t \):
\[
t = \frac{6.42 \times 10^4}{802.50}
\]
Calculating the right side:
1. Calculate \( 6.42 \times 10^4 \):
\[
6.42 \times 10^4 = 64200
\]
2. Now divide by \( 802.50 \):
\[
t = \frac{64200}{802.50} \approx 80
\]
Thus, it will take approximately **80 years** to yield \( 6.42 \times 10^4 \) dollars in interest.