The club's total number of members will grow exponentially each month. she uses the given expression to model the number of club members, in hundreds, after advertising for t months.

1.8(1.02)^12t

what does the value 1.8 represent?

1.8 represents the initial number of the club members in hundreds.

Step-by-step explanation:

* Lets revise the exponential grows

- If a quantity grows by a fixed percent at regular intervals,

 the pattern can be depicted by this function.

- The function of the exponential growth is:

  y = a(1 + r)^x

# a = initial value (the amount before measuring growth)

# r = growth rate (most often represented as a percentage and

  expressed as a decimal)

# x = number of time intervals that have passed

* Now Lets study the problem to solve it

- The club's total number of members will grow exponentially

  each month

- The expression to model the number of club members, in

  hundreds, after advertising for t months is

  1.8(1.02)^12t

* Lets compare between this model and the function above

# a = 1.8 ⇒ initial number of members in hundreds

# r = 1.02 - 1 = 0.02 ⇒ growth rate

# x = 12t ⇒ number of time intervals

* 1.8 represents the initial number of the club members in hundreds.