Question

your uncle says that when he was 10, he used to go down to the fast - food restaurant and get his whole meal for $3. he says, \but that was 40 years ago, i cant believe how much it costs now!\ if the inflation rate is 4%, compounded continuously, how much does he have to pay now? round your answer to the nearest cent (hundredth).

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm.
Here, $P = 3$, $r = 0.04$ (since 4% = 0.04), and $t = 40$.

Step2: Substitute the values into the formula

$A = 3 \times e^{0.04 \times 40}$
First, calculate the exponent: $0.04 \times 40 = 1.6$
Then, $A = 3 \times e^{1.6}$
We know that $e^{1.6} \approx 4.953032424395117$
So, $A = 3 \times 4.953032424395117 \approx 14.85909727318535$

Step3: Round to the nearest cent

Rounding $14.85909727318535$ to the nearest cent (hundredth) gives $14.86$.

Answer:

$\$14.86$