Explanation:
Formula for exponential growth function is written as:
[tex]A_{t}=A_{0}(1+x)^t[/tex], where [tex]A_{t},A_{0}[/tex] are final value and initial value of any substance respectively.
x is the rate at which the substance is increasing.
t = total time for which growth is calculated.
So, if we replace ,[tex](1+x)^t by V^t[/tex] then formula for exponential growth functions will be written as
[tex]A_{t}=A_{0}V^t[/tex],
(a) If , Base =V=1,
[tex]A_{t}=A_{0}1^t=A_{0}[/tex]
The value of the function will remain constant value that is a real number.
(b) If 0<V<1, then
the function becomes decreasing in the interval (0, ∞]. Function almost touches the x axis ,as Asymptote becomes y=0.
We will see that:
A general exponential function can be written as:
f(x) = A*(r)^x
Where r is the base.
We will have:
f(x) = A*(1)^x = A
So we have a constant function.
If 0 < r < 1
We will have that:
[tex]r^x > r^{x +1}[/tex]
Then for:
f(x) = A*(r)^x
We will have that:
f(x) > f(x + 1)
Meaning that as x increases, the function decreases, then we have an exponential decay.
If you want to learn more about exponential functions, you can read:
https://brainly.com/question/11464095
