The graph to an exponential function(Question in description)

Question

The graph to an exponential function f(x) = Cb^x passes the points (1,9/10)and (2, 20/27)

Determine the exact values of C and b.

Answer 1

(1,9/10), (2, 20/27) are two points on an exponential function, f(x) = Cb^x

f(1) = 9/10 = Cb^1 = Cb

Cb = 9/10 Equation I

f(2) = 20/27 = Cb^(2)

Cb^2 = 20/27 Equation II

divide Equation II by Equation I to get

Cb^2/Cb = (20/27)/(9/10)

b = (20/27)(10/9) = 200/243= about0.823

C = (9/10)/b = (9/10)/(20/27)(9/10)= (9/10)(243/200) = 2187/2000=about1.0935

the exponential function is

f(x) = Cb^x

f(x) = (27/20)(200/243)^x

= about 1.35(0.8230452675)^x

= about 1.09(.823)^x