Question

Eli received $10,000 in gift money when he graduated from high school. He deposits the money into an account with a 5 percent
annual interest rate, compounded continuously. Use the formula P(t) = 10,000e^0.05t to determine how much money will be in
his account in four years. Include cents, if needed.

Answer 1

Wrong answer

Answer 2

To find the amount of money in Eli's account after four years, we use the formula P(t) = 10,000e^0.05t.
Substituting t = 4 into the formula, we have P(4) = 10,000e^0.05(4).
P(4) = 10,000e^0.2.
Using a calculator, we find that e^0.2 ≈ 1.2214.
Therefore, P(4) ≈ 10,000(1.2214) = 12,214.
There will be approximately $12,214 in Eli's account after four years. Answer: \boxed{12,214}.

Answer 3

I apologize for the mistake. Let's calculate it correctly:

Using the continuous compounding formula: P(t) = P₀e^(rt)

Where:
P(t) is the amount of money in the account after time t
P₀ is the initial principal (amount deposited) = $10,000
r is the annual interest rate (as a decimal) = 0.05
t is the time in years = 4

P(4) = $10,000 * e^(0.05 * 4)
P(4) ≈ $10,000 * e^(0.2)
Using a calculator, e^(0.2) ≈ 1.2214

P(4) ≈ $10,000 * 1.2214
P(4) ≈ $12,214

Therefore, there will be approximately $12,214 in Eli's account after four years. Answer: $12,214.