your uncle says that when he was 10, he used to go down to the fast - food restaurant and get his whole meal…

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).

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).

Answer

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the annual interest (inflation) rate, and $t$ is the time in years.

Step2: Identify the values of $P$, $r$, and $t$

We are given that $P=$3$, $r = 0.04$ (since $4%=0.04$), and $t = 40$ years.

Step3: Substitute the values into the formula

$A=3\times e^{0.04\times40}$. First, calculate the exponent: $0.04\times40 = 1.6$. Then, find $e^{1.6}$. Using a calculator, $e^{1.6}\approx4.953032424$. Multiply by the initial amount: $A = 3\times4.953032424\approx14.86$.

Answer:

$14.86$