Option B and option C are correct. That are
The growth factor of f(x) is less than the growth factor of g(x).
And, the initial value of f(x) and g(x) are same.
What is exponential function?
A function of the form [tex]A(t) = Ca^{t}[/tex], where a > 0 and a ≠ 1 is an exponential function.
The number C gives the initial value of the function when t = 0.
The number a is the growth or decay factor.
If a> 1, the function represents growth.
If a< 1, the function represents the decay.
According to the given question we have,
two exponential function f(x) and g(x).
[tex]f(x) = 30(1.2)^{x}[/tex]
⇒ growth factor of f(x) = 1.2 ( because 1.2>1 0)
Let, [tex]g(x) = ab^{x}...(i)[/tex]
For the exponential function g(x)
Substitute x = 0 and g(x) = 30 in the above expression
⇒ [tex]30 = a[/tex]
Again, substitute x = 1 and g(x) = 39 in the expression (i)
⇒ [tex]39 = 30(b)^{1}[/tex]
⇒ [tex]b = \frac{39}{30} = 1.3[/tex]
Therefore, the exponential function g(x) is given by
[tex]g(x) = 30(1.3)^{x}[/tex]
⇒ growth factor of g(x) = 1.3
From the definition of the exponential function we know that the C gives the exponential value of the function when t = 0. Here, the initial value of the function f(x) and g(x) is 30 ( when x = 0).
Also, the growth factor of g(x) is greater than the growth factor of f(x) (1.3>1.2).
Hence, option B and option C are correct.
Learn more about the exponential function here:
https://brainly.com/question/11487261
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