Question

an account is opened with $7,595.96 with a rate of increase of 2% per year. after 1 year, the bank account contains $7,746.90. assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years? (round money values to the nearest penny).
y = 7,746.90(0.02)^x
y = 7,595.96(0.02)^x
y = 7,746.90(1.02)^x

Explanation:

Step1: Recall compound growth formula

The standard exponential growth formula for this scenario is $y = P(1 + r)^x$, where $P$ is the initial amount, $r$ is the annual growth rate, and $x$ is time in years.

Step2: Identify correct initial value

The account is opened with an initial amount $P = 7595.96$.

Step3: Calculate growth factor

The annual growth rate is 2%, so $r = 0.02$. The growth factor is $1 + r = 1 + 0.02 = 1.02$.

Step4: Verify with 1-year value

Substitute $x=1$ into $y = 7595.96(1.02)^x$:
$y = 7595.96(1.02)^1 = 7595.96 \times 1.02 = 7746.8792 \approx 7746.90$, which matches the given 1-year amount.

Answer:

$y = 7, 595.96(1.02)^x$ (Note: This is the correct equation corresponding to the scenario, matching the 1-year account value provided)