Mathematics, 10.10.2019 13:20 sierravick123owr441

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 0 and 1?

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Answer from: rebeckas0102

For this case we have a function of the form:
y= A*(b)^x

Where,
A: initial amount
b: rate of change
x: independent variable
y: dependent variable
We then have the following cases of the exponential function.
For $b\ \textgreater \ 1$ :
The exponential function grows
For $b \ \textless \ 1$ :
The exponential function decreases
For b = 1

:
The exponential function does not change

Answer from: izzy488

In exponential growth of functions, the function becomes a constant function if the base of exponents is equal to 1 and the function will become a decreasing function when the value of the base of the exponent lies between $0\text{ and }1$ .

Further explanation:

The exponential function is $y=b^{x}$ .

The behavior of the graph changes with respect to as the graph will increase when and graph will decrease when 0<b<1 .

Given:

In the exponential growth functions the base of the exponent must be greater than .

Calculation:

The exponential growth function is $ab^{x}$ where, is the base of the exponent and is the initial value and is the number of time interval that have passed.

Substitute b=1 in the exponential function.

$\boxed{\begin{aligned}y&=a(1)^{x}\\y&=a\end{aligned}}$

Therefore, the value of the function will be a constant function if the base of the exponent is .

Figure 1 (attached in the end) represents the graph for the case b=1 .

The value of in the exponential functions can be written as,

$\boxed{b=1+r}$ …… (1)

The graph of exponential function where is greater than is shown in the Figure 2 (attached in the end).

The value of in the decay functions can be written as,

$\boxed{b=1-r}$ …… (2)

The term is the rate of change. It can be either growth rate or decay rate.

The value of will vary from to .

If we substitute any value of in the equation (2) then the value of will always lie between to .

Since the graph decreases when 0<b<1 .

Therefore, the exponential function will become a decreasing function if the base of the exponent is between $0\text{ and }1$ .

It can better understand through the graph of $y=ab^{x}$ where, is the real number and the base of the exponent lies between $0\text{ and }1$ is shown in the Figure 3.

Learn more:

1. Learn more about domain and range of the function

2. Learn more about composition of function

3. Learn more about the inverse of the function

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

Keywords: Exponential function, base, exponent, variable, decay function, growth function, decreasing function, increasing function, constant functions, behavior of the graph, base change in exponential function.

In exponential growth functions, the base of the exponent must be greater than 1. how would the func

Answer from: Quest

if you explain the the question more correctly i might be able to answer this better

step-by-step explanation:

Answer from: Quest

What's the denominator

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