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P(t)=1,800(1.004)^(t) 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? Choose 1 answer: (A) $1,836.29 (B) $1,873.31 (c) $2,189.98 (D) $9,036

P(t)=1,800(1.004)t P(t)=1,800(1.004)^{t} \newlineThe function models P P , the amount of money, in dollars, in Yara's savings account t t years after she opened the account with an initial deposit of $1,800 \$ 1,800 . How much money is in Yara's account 55 years after her initial deposit if she makes no deposits or withdraws in that time?\newlineChoose 11 answer:\newline(A) $1,836.29 \$ 1,836.29 \newline(B) $1,873.31 \$ 1,873.31 \newline(C) $2,189.98 \$ 2,189.98 \newline(D) $9,036 \$ 9,036

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Q. P(t)=1,800(1.004)t P(t)=1,800(1.004)^{t} \newlineThe function models P P , the amount of money, in dollars, in Yara's savings account t t years after she opened the account with an initial deposit of $1,800 \$ 1,800 . How much money is in Yara's account 55 years after her initial deposit if she makes no deposits or withdraws in that time?\newlineChoose 11 answer:\newline(A) $1,836.29 \$ 1,836.29 \newline(B) $1,873.31 \$ 1,873.31 \newline(C) $2,189.98 \$ 2,189.98 \newline(D) $9,036 \$ 9,036
  1. Identify function and value: Identify the given function and the value to be substituted.\newlineThe function given is P(t)=1,800(1.004)t P(t) = 1,800(1.004)^t , which models the amount of money in Yara's savings account after t t years. We need to find the amount of money after 5 5 years, so we will substitute t t with 5 5 .
  2. Substitute tt with 55: Substitute tt with 55 in the function to calculate the amount of money after 55 years.\newlineP(5)=1,800(1.004)5P(5) = 1,800(1.004)^5
  3. Calculate (1.004)5(1.004)^5: Calculate the value of (1.004)5(1.004)^5.\newline(1.004)5≈1.02020201(1.004)^5 \approx 1.02020201 (using a calculator for precision)
  4. Multiply by initial deposit: Multiply the initial deposit by the calculated value to find the total amount in the account after 55 years.\newlineP(55) = 1,800×1.020202011,800 \times 1.02020201\newlineP(55) ≈1,836.36362\approx 1,836.36362
  5. Round to two decimal places: Round the result to two decimal places, as we are dealing with currency.\newlineP(5)≈$(1,836.36)P(5) \approx \$(1,836.36)

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