The purchasing power of A dollars after t years of r% inflation is given by the model P $\mathrm { P } = \mathrm { Ae } ^ { - \mathrm { rt } }$ . Assume the inflation rate is currently 6.6%. How long will it take for the purchasing power of $1.00 to be worth $0.67?
Round the answer to the nearest hundredth.
A) 6.07 years
B) 0.61 years
C) 0.06 year
D) 10.15 years

Question

Quizplus · Accepted Answer

To find the time $t$, we use the formula $P = Ae^{-rt}$ with $P = 0.67$, $A = 1$, and $r = 0.066$ (since 6.6% = 0.066). Solving for $t$, we get $0.67 = 1 \cdot e^{-0.066t}$. Taking natural logs of both sides gives $\ln(0.67) = -0.066t$, leading to $t = \frac{\ln(0.67)}{-0.066}$, which approximately equals 6.07 years.

The Purchasing Power of a Dollars After T Years of R