Question

Which of the following statements accurately compares f(x) and g(x)?Choose all that apply.f(x) = 30(1.2)*WNHOg(x)303950.765.913A. The decay factor of f(x) is less than the decay factor of g(x).B. The growth factor of g(x) is less than the growth factor of f(x).C. The growth factor of f(x) is less than the growth factor of g(x).D. The initial values of f(x) and g(x) are the same.

Answer 1

Given that

`f(x)=30(1.2)^x`

To find the value of the function f, substitute the values of x into the given function

Where x = 0

`\begin{gathered} f(0)=30(1.2)^0=30(1)=30 \\ f(0)=30 \end{gathered}`

Where x = 1

`\begin{gathered} f(1)=30(1.2)^1=30(1.2)=36 \\ f(1)=36 \end{gathered}`

Where x = 2

`\begin{gathered} f(2)=30(1.2)^2=30(1.44)=43.2 \\ f(2)=43.2 \end{gathered}`

Where x = 3

`f(3)=30(1.2)^3=30(1.728)=51.84`

From the above deductions,

The initial values of f(x) and g(x) are the same, i.e f(0) and g(0) is 30

The growth factor of f(x) is less than the growth factor of g(x)

Hence, the answers are C and D