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?

Question

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?

Bytelearn · Accepted Answer

Identify variables: Identify the variables in the function. The function P(t) = 1,800(1.004)^(t) models the amount of money in Yara's savings account after t years. Here, P is the amount of money in the account, 1,800 is the initial deposit, 1.004 is the growth factor per year, and t is the number of years.Substitute value: Substitute the given value of t into the function. We need to find the amount of money in the account after 5 years, so we substitute t = 5 into the function: P(5) = 1,800(1.004)^(5).Calculate amount: Calculate the amount of money in the account after 5 years. Using the function with t = 5, we calculate P(5) = 1,800(1.004)^(5). This involves raising 1.004 to the power of 5 and then multiplying the result by 1,800.Perform exponentiation: Perform the exponentiation. Calculate (1.004)^(5) using a calculator or software that can handle exponentiation to ensure accuracy. (1.004)^(5) ≈ 1.02020201Multiply by deposit: Multiply the result of the exponentiation by the initial deposit. Now, multiply the result from Step 4 by the initial deposit of $1,800 to find the total amount in the account after 5 years. P(5) = 1,800 * 1.02020201 ≈ 1,836.36362Round to nearest cent: Round the result to the nearest cent, if necessary, as money is typically represented with two decimal places. P(5) ≈ $1,836.36

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