The equation that shows the relationship between x and y is [tex]y =2(2)^x[/tex]
The table represents an exponential function.
An exponential function is represented as:
[tex]y = ab^x[/tex]
From the table, we have the following ordered pairs
(1,4) and (3,16)
At (1,4), we have:
[tex]ab = 4[/tex]
At (3,16), we have:
[tex]ab^3 = 16[/tex]
Divide both equations
[tex]\frac{ab^3}{ab} = \frac{16}{4}[/tex]
[tex]b^2 = 4[/tex]
Take the square roots of both sides
[tex]b =2[/tex]
Recall that:
[tex]ab =4[/tex]
Make a the subject
[tex]a = \frac 4b[/tex]
So, we have:
[tex]a = \frac 42[/tex]
[tex]a =2[/tex]
Substitute values for a and b in: [tex]y = ab^x[/tex]
[tex]y =2(2)^x[/tex]
Hence, the equation that shows the relationship between x and y is [tex]y =2(2)^x[/tex]
Read more about exponential functions at:
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