The exponential function that represents the table is [tex]y =18 (\frac 65)^x[/tex]
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where:
- a represents the initial value
- b represents the rate
From the table we have the following ordered pair
(x,y) = {(0,18) (1,21.6)}
So, we have:
[tex]y = ab^x[/tex]
[tex]18 = a \times b^0[/tex]
[tex]a= 18[/tex]
Also, we have:
[tex]y = ab^x[/tex]
[tex]21.6 = a \times b^1[/tex]
[tex]21.6 = 18 \times b[/tex]
Divide both sides by 18
[tex]b = 1.2[/tex]
So, we have:
[tex]y =18 \times 1.2^x[/tex]
Rewrite as:
[tex]y =18 (\frac 65)^x[/tex]
Hence, the exponential function that represents the table is [tex]y =18 (\frac 65)^x[/tex]
Read more about exponential functions at:
https://brainly.com/question/11464095
