Question

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 submit

Explanation:

Step1: Identify the formula for exponential decay

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.
Here, \( P = 85630 \), \( r = 0.08 \) (since 8% = 0.08), and \( t = 8 \).

Step2: Substitute the values into the formula

Substitute \( P = 85630 \), \( r = 0.08 \), and \( t = 8 \) into the formula:
\( A = 85630(1 - 0.08)^8 \)
First, calculate \( 1 - 0.08 = 0.92 \).
Then, calculate \( 0.92^8 \). Let's compute \( 0.92^8 \approx 0.513215597 \).

Step3: Calculate the final amount

Multiply \( 85630 \) by \( 0.513215597 \):
\( A = 85630 \times 0.513215597 \approx 43946.65 \)

Step4: Round to the nearest whole number

Rounding \( 43946.65 \) to the nearest whole number gives \( 43947 \).

Answer:

43947