Find the equation of the exponential function that goes through the points (0,2000) and (2,20).

Question

Find the equation of the exponential function that goes through the points (0,2000) and (2,20).

Answer 1

(0, 2000), (2, 20) are two points on an exponential function

f(x) = ab^x

f(0) = ab^x = ab^0 = a = 2000

f(2) = ab^x = 2000b^x = 20

100b^2 = 1

b^2 = 1/100

b = 1/10 =0,1

f(x) = 2000(0.1)^x is an exponential function through the 2 given points