Question

Write an equation that shows the relationship between x and y.

Answer 1

The equation that shows the relationship between x and y is $y =2(2)^x$

The table represents an exponential function.

An exponential function is represented as:

$y = ab^x$

From the table, we have the following ordered pairs

(1,4) and (3,16)

At (1,4), we have:

$ab = 4$

At (3,16), we have:

$ab^3 = 16$

Divide both equations

$\frac{ab^3}{ab} = \frac{16}{4}$

$b^2 = 4$

Take the square roots of both sides

$b =2$

Recall that:

$ab =4$

Make a the subject

$a = \frac 4b$

So, we have:

$a = \frac 42$

$a =2$

Substitute values for a and b in: $y = ab^x$

$y =2(2)^x$

Hence, the equation that shows the relationship between x and y is $y =2(2)^x$

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