Question

a customer deposits $1,000 in an account in which the interest is compounded annually. the table below shows the balances in the account at the end of each year.

amount in account vs. number of years
\

$$\begin{tabular}{|c|c|} \\hline \\text{amount in account, } a & \\text{number of years after initial deposit, } t \\\\ \\hline 1,000 & 0 \\\\ \\hline 1,080 & 1 \\\\ \\hline 1,166.40 & 2 \\\\ \\hline 1,259.71 & 3 \\\\ \\hline 1,360.49 & 4 \\\\ \\hline \\end{tabular}$$

which equation best represents the data in the table?

\\(a = 1000(1.08)^t\\)
\\(a = 1080^t\\)
\\(a = 1000(1.8)^t\\)
\\(a = 800^t\\)

Explanation:

Determine the initial value and growth factor

$$
LATEXBLOCK0
$$

Formulate the exponential equation

$$ A = 1000(1.08)^t $$

Verify with subsequent data points

$$
LATEXBLOCK1
$$

Answer:

• (A) \(A = 1000(1.08)^t\) (Correct answer)
• (B) \(A = 1080^t\)
• (C) \(A = 1000(1.8)^t\)
• (D) \(A = 800^t\)