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

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

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,

$2 = 4b$

$b = \frac{2}{4}$

$b = \frac{1}{2}$

or

$b = 0.5$

We substitute back to get,

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

The correct answer is D.