Question

subscriptions to a fashion magazine have gone down by a consistent 7% each year. if the magazine currently has 28,215 subscribers, how many will there be in 4 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.

Step2: Convert the decay rate to a decimal

The decay rate is 7%, so \( r = \frac{7}{100} = 0.07 \).

Step3: Identify the initial amount and time

The initial amount \( P = 28215 \) and the time \( t = 4 \) years.

Step4: Substitute the values into the formula

Substitute \( P = 28215 \), \( r = 0.07 \), and \( t = 4 \) into the formula:
\( A = 28215(1 - 0.07)^4 \)
\( A = 28215(0.93)^4 \)

Step5: Calculate \( (0.93)^4 \)

First, calculate \( 0.93^2 = 0.8649 \), then \( 0.8649^2 = 0.74789701 \) (or directly calculate \( 0.93^4 = 0.93\times0.93\times0.93\times0.93 = 0.74789701 \))

Step6: Calculate the final amount

Multiply \( 28215 \) by \( 0.74789701 \):
\( A = 28215\times0.74789701 \approx 28215\times0.7479 \)
\( 28215\times0.7479 = 28215\times(0.7 + 0.04 + 0.007 + 0.0009) \)
\( = 28215\times0.7 + 28215\times0.04 + 28215\times0.007 + 28215\times0.0009 \)
\( = 19750.5 + 1128.6 + 197.505 + 25.3935 \)
\( = 19750.5 + 1128.6 = 20879.1 \); \( 20879.1 + 197.505 = 21076.605 \); \( 21076.605 + 25.3935 = 21101.9985 \approx 21102 \) (or use a calculator for a more precise multiplication: \( 28215\times0.74789701 \approx 21102 \))

Answer:

21102