To calculate how much Matthew has in his account after 3 years with the given compound interest formula, we need to identify the variables in the formula:
- \( P \) = principal amount (initial investment) = $5000
- \( i \) = interest rate (as a decimal) = 3.8% = 0.038
- \( t \) = number of years = 3
The formula for compound interest is:
\[ A(t) = P(1 + i)^{t} \]
Now we can substitute the values into the formula:
\[ A(3) = 5000(1 + 0.038)^{3} \]
First, calculate \( 1 + 0.038 \):
\[ 1 + 0.038 = 1.038 \]
Now raise that to the power of 3:
\[ (1.038)^{3} \approx 1.117 \]
Next, multiply that by the principal amount:
\[ A(3) = 5000 \times 1.117 \approx 5585 \]
Therefore, after 3 years, Matthew will have approximately:
\[ \boxed{5585} \]