subscriptions to a fashion magazine have gone down by a consistent 9% each year. if the magazine currently…
subscriptions to a fashion magazine have gone down by a consistent 9% each year. if the magazine currently has 74,703 subscribers, how many will there be in 10 years? if necessary, round your answer to the nearest whole number. subscribers
Answer
Explanation:
Step1: Identify the formula
The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time in years.
Step2: Convert the rate to a decimal
The rate of decay $r = 9%=0.09$. The initial number of subscribers $P = 74703$ and the time $t = 10$ years.
Step3: Substitute values into the formula
$A=74703\times(1 - 0.09)^{10}=74703\times0.91^{10}$.
Step4: Calculate $0.91^{10}$
$0.91^{10}\approx0.408468$.
Step5: Calculate the final number of subscribers
$A = 74703\times0.408468\approx30515$.
Answer:
30515