a publishing industry report predicts that magazine subscriptions will drop by 8% each year. if this…

a publishing industry report predicts that magazine subscriptions will drop by 8% each year. if this prediction is correct, then how many subscribers will a magazine with 85,630 subscribers have in 8 years? if necessary, round your answer to the nearest whole number. subscribers

a publishing industry report predicts that magazine subscriptions will drop by 8% each year. if this prediction is correct, then how many subscribers will a magazine with 85,630 subscribers have in 8 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 percentage to a decimal

The rate of decay $r = 8%=0.08$, the initial number of subscribers $P = 85630$, and the time $t = 8$ years.

Step3: Substitute the values into the formula

$A=85630\times(1 - 0.08)^8$. First, calculate $1-0.08 = 0.92$. Then, $(0.92)^8=0.5132228709$. Next, $A = 85630\times0.5132228709$. $A=43957.07454$.

Step4: Round the answer

Rounding $43957.07454$ to the nearest whole number gives $43957$.

Answer:

$43957$