The exponential function h, whose graph is given below, can be written as

h(x) = a * b^x

Complete the equation for h(x)

Answer

h(x) = 6 * (2/3)^x

Steps:

The graph specifically highlights two points that might interest us in obtaining the equation. They are x=0 and x=1.

For x=0,
h(x) = 6 {obtained from the graph}
h(x) = 6 = a*b^0
Implies, a=6, since anything to the power 0 is 1, therefore b^0 is 1.

For x=1,
h(x) = 4 {obtained from the graph}
h(x) = 4 = 6*b^1 {a substituted by 6}
Implies, 4=6*b, since anything to the power 1 is itself, therefore b^1 is b.

b then is given by 4/6, simplified to 2/3.

Therefore the equation then becomes,

h(x) = 6 * (2/3)^x