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(1.02)^x\\)
\\(y = 7,746.90(0.02)^x\\)
\\(y = 7,595.96(1.02)^x\\)
\\(y = 7,595.96(0.02)^x\\)

Explanation:

Identify the initial value

$$ a = 7595.96 $$

Determine the growth factor

$$ b = 1 + r = 1 + 0.02 = 1.02 $$

Formulate the exponential equation

$$ y = 7595.96(1.02)^x $$

Answer:

• (A) \(y = 7,746.90(1.02)^x\)
• (B) \(y = 7,746.90(0.02)^x\)
• (C) \(y = 7,595.96(1.02)^x\) (Correct answer)
• (D) \(y = 7,595.96(0.02)^x\)