a publishing industry report predicts that magazine subscriptions will drop by 10% each year. if this…

a publishing industry report predicts that magazine subscriptions will drop by 10% each year. if this prediction is correct, then how many subscribers will a magazine with 98,000 subscribers have in 10 years? (round to the nearest whole number if necessary).

a publishing industry report predicts that magazine subscriptions will drop by 10% each year. if this prediction is correct, then how many subscribers will a magazine with 98,000 subscribers have in 10 years? (round to the nearest whole number if necessary).

Answer

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.

Step2: Determine the values of $P$, $r$, and $t$

$P = 98000$, $r=0.1$ (since 10% = 0.1), and $t = 10$.

Step3: Substitute the values into the formula

$A=98000\times(1 - 0.1)^{10}=98000\times0.9^{10}$.

Step4: Calculate $0.9^{10}$

$0.9^{10}=0.3486784401$.

Step5: Calculate $A$

$A = 98000\times0.3486784401\approx34170$.

Answer:

34170