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:

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<reasoning>

Identify the initial value

\[
a = 7595.96
\]

Determine the growth factor

\[
b = 1 + r = 1 + 0.02 = 1.02
\]

Formulate the exponential equation

\[
y = 7595.96(1.02)^x
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = 7,746.90(1.02)^x\)</mcq-option>
<mcq-option>(B) \(y = 7,746.90(0.02)^x\)</mcq-option>
<mcq-correct>(C) \(y = 7,595.96(1.02)^x\)</mcq-correct>
<mcq-option>(D) \(y = 7,595.96(0.02)^x\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the initial value

\[
a = 7595.96
\]

Determine the growth factor

\[
b = 1 + r = 1 + 0.02 = 1.02
\]

Formulate the exponential equation

\[
y = 7595.96(1.02)^x
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = 7,746.90(1.02)^x\)</mcq-option>
<mcq-option>(B) \(y = 7,746.90(0.02)^x\)</mcq-option>
<mcq-correct>(C) \(y = 7,595.96(1.02)^x\)</mcq-correct>
<mcq-option>(D) \(y = 7,595.96(0.02)^x\)</mcq-option>
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