The exponential function h, whose graph is given below, can be written as h(x)=a•b^x. complete the equation for h(x).

h(x) = a.b^x

h(1) = 2 = a.b^1 = ab

h(0) = 4 = a.b^0 = a

So,

a = 4

ab = 2

4.b = 2

b = 2/4

b = 1/2

h(x) = 4.(1/2)^x

h(x) = 2².(2^(-1))^x

h(x) = 2^2.2^(-x)

h(x) = 2^(2 - x)

h(x) = 2^(2 - x).

Step-by-step explanation:

h(x) = a.b^x

At h(1)

h(1) = a.b^1

h(1) = ab

Since h(1) = 2, then

2 = ab

ab = 2eqn 1

At h(0)

h(0)= a.b^0

h(0) = a.1

h(0) = a

Since h(0) = 4, then

4 = a

a = 4eqn 2

So we subtitle for b in eqn 1.

I.e

ab = 2 , where a = 4 from eqn 2

ab = 2

= 4b = 2

b = 2/4 = 1/2

Therefore:

h(x) = a.b^x

Since we have value for a and b.

h(x) = 2².(1/2)^x

h(x) = 2².(2^(-1))^x

h(x) = 2^2.2^(-x)

h(x) = 2^(2 - x).

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step-by-step explanation:

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