Question

Exponential Functions: Identify all components of the standardform of an exponential function equation. Using an exponentialequation create a table of values and a graph to represent theequation chosen.

Answer 1

Let's take a random exponential function.

Take the function:

`y=10(1.25)^x`

Now, let's identify all the components.

The standard form of an exponential function is

`y=A(b)^x`

Where:

y is the final value

A is the initial value

b is the growth/decay factor

If b> 1 the function shows growth, if b < 1, the function shows decay.

x is the input variable.

Comparing both equations we have:

Initial value = 10

Growth factor = 1.25

Now, let's create a table of values.

We have:

`\begin{gathered} When\text{ x = 0: y}=10(1.25)^0=10 \\ \\ When\text{ x = 1: y}=10(1.25)^1=12.5 \\ \\ when\text{ x = 2: y = 10\lparen1.25\rparen}^2=15.625 \\ \\ When\text{ x = 3:y=10\lparen1.25\rparen}^3=19.53 \end{gathered}`

Hence, we have the table:

x y

0 10

1 12.5

2 15.625

3 19.3

The graph is shown below: