Is the function below exponential?
G(t)=(5⋅t)^2
If so, write the function in the form G(t)=ab^t and enter the values you find for a and b in the indicated blanks below. If the function is not exponential, enter NONE in both blanks below.
a=
b=
The function G(t) = (5⋅t)^2 is not exponential. Therefore, we enter NONE in both blanks for a and b.
a = NONE
b = NONE
To determine if the function G(t)=(5⋅t)^2 is exponential, we need to check if it can be written in the form G(t) = a⋅b^t, where a and b are constants.
First, let's simplify the given function:
G(t) = (5⋅t)^2
= 25⋅t^2
We can see that the function is not in the form a⋅b^t. It is a quadratic function instead, where the variable is squared. Therefore, the function G(t)=(5⋅t)^2 is not exponential.
Thus, both blanks should be filled with NONE.