as a result of inflation, the purchasing power of a fixed quantity of money decreases by 5% every year. if a…
as a result of inflation, the purchasing power of a fixed quantity of money decreases by 5% every year. if a certain quantity of money can buy 175 frozen dinners this year, how many frozen dinners can it buy in 12 years? if necessary, round your answer to the nearest whole number. frozen dinners
Answer
Answer:
89
Explanation:
Step1: Identify the decay - formula
The formula for exponential decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 175$, $r=0.05$, and $t = 12$.
Step2: Substitute the values into the formula
$A=175\times(1 - 0.05)^{12}=175\times(0.95)^{12}$.
Step3: Calculate $(0.95)^{12}$
$(0.95)^{12}\approx0.5085$.
Step4: Calculate the final amount
$A = 175\times0.5085=88.9875\approx89$.