Let's take a random exponential function.
Take the function:
[tex]y=10(1.25)^x[/tex]Now, let's identify all the components.
The standard form of an exponential function is
[tex]y=A(b)^x[/tex]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:
[tex]\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}[/tex]Hence, we have the table:
x y
0 10
1 12.5
2 15.625
3 19.3
The graph is shown below:
