Question

Sam has 3,250 followers on social media, and his number of followers is decreasing at a rate of 3% per week. Which function represents his number of followers after w weeks?

A) f(w) = 3,250(0.97)^w
B) f(w) = 3,250(1.03)^w
C) f(w) = 3,250(1.03) - 1
D) f(w) = 3,250(0.97)

Answer 1

The correct function representing the number of Sam's followers after w weeks, considering a 3% weekly decrease, is A) f(w) = 3,250(0.97)^w, which shows an exponential decay.

Step-by-step explanation:

The question involves finding the function that represents the number of followers Sam has on social media after w weeks, given that his number of followers is decreasing at a rate of 3% per week. The correct function is A) f(w) = 3,250(0.97)^w because each week represents a decrease to 97% of the number of followers from the previous week (which is a 3% decrease). This function models an exponential decay where the base of the exponent is less than 1, reflecting a decrease in the value of the function over time.

The correct function that represents Sam's number of followers after w weeks is f(w) = 3,250(0.97)^w (option A).

Here's the rationale:

Sam's number of followers is initially 3,250.

The 3% weekly decrease signifies that the number of followers is multiplied by 0.97 each week (100% - 3% = 97%).

The exponent w represents the number of weeks, and since the followers are decreasing each week, the exponent w is positive.

Multiplying 3,250 by 0.97 for each week represents the decreasing trend, which is correctly reflected in option A: f(w) = 3,250(0.97)^w.