Digital PSAT Math Practice Question 278: Answer and Explanation

Question: 278

A business starts a social media account at the beginning of the year, beginning with 100 followers. With each month that passes, the number of followers increases by 5%, compounding on the previous month's total number of followers. Which would best represent the relationship between months and the number of followers?

• A. An exponentially increasing relationship
• B. An exponentially decreasing relationship
• C. A linear relationship, with the line of the relationship having a constant slope
• D. A linear relationship, with the line of the relationship having a positive, changing slope

Correct Answer: A

Explanation:

(A) Calculate the number of followers in the first few months and see if you can find a pattern.

In the beginning, or month 0, there are 100 followers.

After month 1, the number of followers increases by 5%, so there are now

1.05(100) = 105 followers.

After month 2, the number of followers increases by 5% again, giving 1.05(105) followers.

Since 105 = 1.05(100) based on your calculation in the previous month, you can substitute this expression in for 105 to get that the number of followers is 1.05(1.05(100)), or (1.05)² (100) followers.

Similarly, you get that the number of followers in month 3 is (1.05)³(100). Continuing in this manner, a pattern emerges, giving you a formula for the number of followers in month n: (1.05)ⁿ(100). This is an exponential relationship between months and number of followers since the months variable is the exponent in your function. Also, the number of followers increases each month, so this is an exponentially increasing relationship. This matches choice (A).