A bank deposit yields $802.50 in interest every year. How many years will it take to yield 6.42×104

Question

dollars? Write the answer in scientific notation.(1 point)
Responses

1.25×102
1 point 2 5 times 10 squared

8×104
8 times 10 to the 4th power

8×101
8 times 10 to the 1th power

8×102

Answer 1

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

\[ \text{Years} = \frac{\text{Total Interest}}{\text{Interest per Year}} \]

In this case:

• Total Interest = \( 6.42 \times 10^4 \)
• Interest per Year = \( 802.50 \)

Now we can calculate the number of years:

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

Calculating the division:

1. First, we can convert \( 802.50 \) into scientific notation:
   \( 802.50 = 8.025 \times 10^2 \)

2. Now, we can perform the division:

\[ \text{Years} = \frac{6.42 \times 10^4}{8.025 \times 10^2} \]

3. Dividing the coefficients and subtracting the exponents gives:

\[ \text{Years} = \frac{6.42}{8.025} \times 10^{4-2} \approx 0.800 \times 10^2 \]

4. Converting \( 0.800 \) into proper scientific notation gives:

\[ \text{Years} \approx 8.00 \times 10^1 \]

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

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