Solving Exponential Equations Quick Check

Question

3 of 53 of 5 Items
Question
A bank account earns 3% interest per year. If you deposit $1,000 into the account, what equation would you use to determine how much will be in the account after 5 years?(1 point)
Responses

y=1,000(1.03)5
y equals 1,000 left parenthesis 1.03 right parenthesis superscript 5 baseline

y=5(1.03)1,000
y equals 5 left parenthesis 1.03 right parenthesis superscript 1,000 baseline

y=5(0.03)1,000
y equals 5 left parenthesis 0.03 right parenthesis superscript 1,000 baseline

y=1,000(0.03)5

Answer 1

To determine how much will be in the bank account after 5 years with an initial deposit of $1,000 that earns 3% interest per year, you would use the formula for compound interest, which is:

\[ y = P(1 + r)^t \]

Where:

• \( P \) is the principal amount (the initial deposit)
• \( r \) is the annual interest rate (in decimal)
• \( t \) is the time in years

For this particular question:

• \( P = 1,000 \)
• \( r = 0.03 \) (which is 3% expressed as a decimal)
• \( t = 5 \)

Thus, the equation becomes:

\[ y = 1,000(1 + 0.03)^5 = 1,000(1.03)^5 \]

Therefore, the correct response is:

y = 1,000(1.03)⁵