Exponential Functions

Question

find an exponential function of the form f(x)=ab^x that passes through the given points: (1,1), (2, 2/5), (3, 4/25)

Answer 1

f(x) = ab^x

1 = ab¹

1/b = a

 

2/5 = (1/b)(b²)

2/5 = b

 

f(x) = (5/2)(2/5)^x

 

Check:

 

4/25 = (5/)(2/5)³

4/25 = (2/5)²

4/25 = 4/25