twelve years ago, a candy bar at a gas station costs $0.85. if the inflation rate is 7.5%, compounded…

Explanation:

Step1: Identify the 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 have $P = 0.85$, $r=0.075$ (since $7.5%= 0.075$), and $t = 12$.

Step3: Substitute the values into the formula

$A=0.85\times e^{0.075\times12}$. First, calculate the exponent: $0.075\times12 = 0.9$. Then, find $e^{0.9}\approx2.45960311$. Multiply by $P$: $A = 0.85\times2.45960311\approx2.09$.

Answer:

$$2.09$