Question

When it was first started, the Clinton High Cooking Club had 10 members. Each year after the club started, the number of members increased by a factor of approximately 1.2. Write a function that gives the number m(t) of members in the cooking club t years after it started.

a) m(t) = 10 × (1.2)^t

b) m(t) = 10 + 1.2t

c) m(t) = 10t × 1.2

d) m(t) = 10 ÷ (1.2)^t

Answer 1

The function that models the number of members in the cooking club after t years with an initial 10 members and an annual increase factor of 1.2 is a. m(t) = 10 × (1.2)^t.

Step-by-step explanation:

The student is looking to write a function m(t) that represents the number of members in the cooking club t years after it started, with the number of members increasing annually by a factor of approximately 1.2. The correct representation of this scenario is an exponential growth function. Given the initial value of 10 members and a growth factor of 1.2, the function that correctly models this situation is:

m(t) = 10 × (1.2)^t

This function indicates that to find the number of members after t years, you multiply the initial number of members (10) by 1.2 raised to the power of t (the number of years since the club started).