Question

Describe how the graph of f(x) = ab* changes for a givenpositive value of a as you increase the value of b when b > 1. Discuss the riseand fall of the graph and the y-intercept.When

Answer 1

An exponential function can be described as a function that grows or shrinks at a constant percent growth rate. It can be modeled using the formula:

`f(x)=a(b)^x`

where a is the initial or starting value and b is the growth factor or growth multiplier.

An exponential function can either model growth or decay. If it models growth b > 1 and a decay if 0 < b < 1.

The question, on the basis of the explanation above, represents an exponential growth model. The growth of the function is based on the growth multiplier, b. A higher value of b means that the graph becomes steeper.

Note that regardless of the value of b, the starting point of the graph, if it remains the same, will be unchanged, meaning that the y-intercept will not change with a change in the growth multiplier.

Consider the function below:

`f(x)=2(3)^x`

In the function, the growth multiplier is 3. We can increase this value by one unit to get 2 other functions such that:

`\begin{gathered} g(x)=2(4)^x \\ h(x)=2(5)^x \end{gathered}`

The graphs of the 3 functions are shown below:

We can see that the graph becomes steeper with an increase in b while the y-intercept remains the same.

ANSWER

The graph will rise quicker with an increase in the value of b, while the y-intercept will remain unchanged.