Question

In exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1? How would the function change if the base of the exponent were between 0and 1?

Answer 1

If the base were 1, then the final value would never change...it would be a constant...

If the base is between zero and one, it is an exponential decay equation, so the final value would continually get smaller and smaller...

Answer 2

Explanation:

Formula for exponential growth function is written as:

$A_{t}=A_{0}(1+x)^t$, where $A_{t},A_{0}$ 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 ,$(1+x)^t by V^t$ then formula for exponential growth functions will be written as

$A_{t}=A_{0}V^t$,

(a) If , Base =V=1,

$A_{t}=A_{0}1^t=A_{0}$

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.