Question

The formula for the number of students in the Key Club each year, starting with 10 students and doubling each year, can be written as:

A) S_n = 10 * 2^n
B) S_n = 10 * (n + 1)
C) S_n = 10 * n^2
D) S_n = 10 * n

Answer 1

The correct formula for the number of students in the Key Club that starts with 10 and doubles each year is S_n = 10 × 2^n, representing exponential growth with 2 as the base of the exponent.

Step-by-step explanation:

The student is dealing with a mathematical problem that involves an exponential growth pattern. The formula to represent the number of students in the Key Club, which starts with 10 and doubles each year, can be written as S_n = 10 × 2^n.

This is an example of an exponential function where the base of the exponent represents the rate of growth, which is 2 in this case because the number of students doubles each year. The variable n represents the number of years that have passed. The correct formula reflects this exponential growth accurately.