Question

a social networking site currently has 40,912 active members per month, but that figure is dropping by 5% with every month that passes. how many active members can the site expect to have in 10 months? if necessary, round your answer to the nearest whole number. active members 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 period.
Here, \( P = 40912 \), \( r = 0.05 \) (since 5% = 0.05), and \( t = 10 \).

Step2: Substitute the values into the formula

Substitute \( P = 40912 \), \( r = 0.05 \), and \( t = 10 \) into the formula:
\( A = 40912(1 - 0.05)^{10} \)
First, calculate \( 1 - 0.05 = 0.95 \).
Then, calculate \( 0.95^{10} \). Using a calculator, \( 0.95^{10} \approx 0.5987369392 \).

Step3: Calculate the final amount

Multiply \( 40912 \) by \( 0.5987369392 \):
\( A = 40912 \times 0.5987369392 \approx 40912 \times 0.598737 \)
\( 40912 \times 0.598737 \approx 24495.5 \) (rounded to one decimal place for intermediate step)
Rounding to the nearest whole number, we get \( A \approx 24496 \).

Answer:

24496