What is the exponential function f(x)=Ca^x

Question

whose graph goes through the points (0,2) and (2,8)?

 

 

Answer 1

The points are (0, 2) and (2, 8)

The exponential function f(x) = Ca^x

y = Ca^x

Substitute for (x, y) = (0 , 2) in y = Ca^x

2 = Ca⁰

C = 2 ---> (1)

Substitute for (x, y) = (2 , 8) in y = Ca^x

8 = Ca²

From equation (1), substitute c = 2.

8 = 2a²

a² = 4

a = ± 2

From the definition of exponential function a > 0, so consider a = 2.

Substitute a = 2, c = 2 in f(x) = Ca^x

Required function is f(x) = 2(2)^x .