Question

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

Answer 1

Answer:
`y=2^(5+2x)`Step-by-step 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} (8)/(2)=(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=(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*2^(2x) \\ y=2^(5+2x) \end{gathered}`

The function is:

`y=2^(5+2x)`