Question

The expression f(x) = 12(1.035)* models the monthly growth of membership in the new drama club at a school. According to the function, what is the monthly growth rate?

Answer 1

The monthly growth rate is 3.5%.

Explanation:

The exponential growth function is given as follows:

`y=a(1+r)^(x)`

Here,

y = final value

a = initial value

r = growth rate

x = time taken

The provided expression for the monthly growth of membership in the new drama club at a school is:

`f(x) = 12\cdot(1.035)^(x)`

Comparing this function with the exponential growth function:

`a(1+r)^(x)=12(1.035)^(x)\\\\a(1+r)^(x)=12(1+0.035)^(x)`

Then value of r is 0.035 or 3.5%.

Thus, the monthly growth rate is 3.5%.