Question

I need help with number 10 please I already have number 9 done :)

Answer 1

Answer:$y=2^{5+2x}$Explanation:

From the relationship given, the equation has a constant ratio, b = 8/2

b = 4

This is an exponential relationship of the form:

$y=ab^x$

Substitute the points (-2, 2) and (-1, 8) into the equation to get a and b

For (-2, 2)

x = -2, y = 2

$2=ab^{-2}\ldots\ldots\text{.}(1)$

For (-1, 8)

x = -1, y = 8

$8=ab^{-1}\ldots\ldots\ldots\ldots.\ldots\ldots\ldots\ldots\ldots\text{.}(2)$

Divide equation (2) by equation (1)

$\begin{gathered} \frac{8}{2}=\frac{ab^{-1}}{ab^{-2}} \\ 4=b \\ b\text{ = 4} \end{gathered}$

Substitute b = 4 into equation (2)

$\begin{gathered} 8=ab^{-1} \\ 8=a(4^{-1}) \\ 8=\frac{a}{4} \\ a=4(8) \\ a=32 \end{gathered}$

Substitute a = 32 and b = 4 into the original exponential equation

$\begin{gathered} y=ab^x \\ y=32(4^x) \\ y=2^5\times2^{2x} \\ y=2^{5+2x} \end{gathered}$

The function is:

$y=2^{5+2x}$