Question

Use two points to write an equation for each function shown NEED HELP FILLING THIS OUT!!!?

Answer 1

I think that the answer is C

Answer 2

The required answer for blank 1 is
`(1)/(2)`, for blank 2 is
`(1)/(2)`, for blank 3 is 0, for blank 4 is 1 and for blank 5 is
`((1)/(2))^x`.

Explanation:

From the given table it is noticed that the value of function f(x) at x=-1 is 2 and the value of function f(x) at x=-2 is 4.

The exponential function is defined as

`f(x)=ab^x`

Where, a is initial value and b is growth factor.

`(f(-1))/(f(-2))=(2)/(4)=(1)/(2)`

Therefore the required answer for blank 1 is
`(1)/(2)`.

So, the growth rate is
`b=(1)/(2)`.

Since a is the initial value, therefore

`a=f(0)=1`

Therefore the exponential function is

`f(x)=(1)((1)/(2))^x`

`f(x)=((1)/(2))^x`

Therefore required answer for blank 1 is
`(1)/(2)`, for blank 2 is
`(1)/(2)`, for blank 3 is 0, for blank 4 is 1 and for blank 5 is
`((1)/(2))^x`.