Exponential expressions word problems (algebraic)
Google Classroom
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 $\mathrm{m}(\mathrm{t})$ of members in the cooking club $t$ years after it started.
\[
m(t)=
\]
Stuck? Review related articles/videos or use a hint.
Report a problem

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 ：\(\boxed{m(t) = 10 \cdot 1.2^t}\)