Given the two points (1, 3) and (2, 4.5), find the equation of the exponential function that passes through these two points.

Question

Given the two points (1, 3) and (2, 4.5), find the equation of the exponential function that passes through these two points.

Answer 1

(1,3) and (2, 4.5) are two points on the graph of an exponential function y= ab^x

3= ab, a = 3/b

4.5 = ab^2, a = 4.5/b^2

3/b = 4.5/b^2

3 =4.5/b

b = 4.5/3 = 1.5

a = 3/1.5 = 2

the exponential function is f(x) = 2(1.5)^x

3 = 2(1.5)^1 = 2(1.5) = 3

4.5 = 2(1.5)^2 = 2(2.25) = 4.5