Question

A. f(x)=4*2^x
B.f(x)=0.5*(4)^x
C.f(x)=2*(0.5)^x
D.f(x)=4*(0.5)^x

Answer 1

ANSWER
The answer is D


`f(x) = 4{(0.5)}^(x)`

Step-by-step explanation

Let the exponential function be of the form


`f(x) = a {b}^(x)`

Each box on both the x and y axes is one unit.

The graph passes through the point
`(0,4)`.

This point must satisfy the equation above.


`4 = a {b}^(0)`

This implies that,


`4 = a(1)`


`a = 4`

The function now becomes,


`f(x) = 4 {(b})^(x)`

The graph also passes through


`(1,2).`

We substitute this point too to get,


`2 = 4 {b}^(1)`

This implies that,


`2 = 4b`


`b = (2)/(4)`


`b = (1)/(2)`

or


`b = 0.5`

We substitute back to get,


`f(x) = 4 {(0.5})^(x)`

The correct answer is D.