$P(t) = 1,800(1.004)^t$ $\newline$ The function models $P$ , the amount of money, in dollars, in Yara's savings account $t$ years after she opened the account with an initial deposit of $\$1,800$ . How much money is in Yara's account $5$ years after her initial deposit if she makes no deposits or withdraws in that time? $\newline$ Choose $1$ answer: $\newline$ (A) $\$1,836.29$ $\newline$ (B) $\$1,873.31$ $\newline$ (C) $\$2,189.98$ $\newline$ (D) $\$9,036$

Full solution

P(t) = 1,800(1.004)^t

\newline

The function models

P

, the amount of money, in dollars, in Yara's savings account

t

years after she opened the account with an initial deposit of

\$1,800

. How much money is in Yara's account

5

years after her initial deposit if she makes no deposits or withdraws in that time?

\newline

Choose

1

answer:

\newline

(A)

\$1,836.29

\newline

(B)

\$1,873.31

\newline

(C)

\$2,189.98

\newline

(D)

\$9,036

Given Function Calculation: Given the function $P(t) = 1,800(1.004)^{t}$ , we need to calculate the amount of money in Yara's account after $5$ years. We will substitute $t$ with $5$ in the function to find $P(5)$ .
Substitute $t$ with $5$ : Perform the calculation for $P(5)$ using the given function: $\newline$ $P(5) = 1,800(1.004)^{(5)}$
Evaluate Expression: Use a calculator or a computational tool to evaluate the expression: $P(5) = 1,800 \times (1.004)^5$
Multiply Result: After calculating the expression, we get: $P(5) \approx 1,800 \times 1.02020201$
Round to Two Decimal Places: Now, multiply $1,800$ by $1.02020201$ to find the final amount: $\newline$ $P(5) \approx 1,800 \times 1.02020201 \approx 1,836.36362$
Compare with Answer Choices: Round the result to two decimal places to match the answer choices: $P(5) \approx \$1,836.36$
Compare with Answer Choices: Round the result to two decimal places to match the answer choices: $\newline$ $P(5) \approx \$1,836.36$ Compare the result with the given answer choices: $\newline$ (A) $\$1,836.29$ $\newline$ (B) $\$1,873.31$ $\newline$ (C) $\$2,189.98$ $\newline$ (D) $\$9,036$ $\newline$ The closest answer to our calculation is (A) $\$1,836.29$ .