Step 1 :The problem is asking for a function that models the growth of the club's membership over time. The initial number of members is 10, and each year the number of members increases by a factor of 1.2. This is an example of exponential growth, and the general form of an exponential function is \(f(t) = a \cdot b^t\), where \(a\) is the initial amount, \(b\) is the growth factor, and \(t\) is time. In this case, \(a = 10\) and \(b = 1.2\).
Step 2 :The function \(m(t)\) correctly models the growth of the club's membership over time. It takes the number of years since the club started as input and returns the number of members in the club at that time.
Step 3 :\(\boxed{m(t) = 10 \cdot 1.2^t}\)