Absolute and relative growth rates Two functions f and g are given. Show that the growth rate of the linear function is constant and the relative growth rate of the exponential function is constant.

f(t) = 2200 + 400t, g(t)= 400 · 2t/20

Solution 10E Step 1 In this problem we have to show that the growth rate of the linear function is constant and the relative growth rate of the exponential function is constant. Given f(t) = 2200 + 400t which is linear And g(t) = 400(2 t/2) which is exponential. To prove: t he growth rate of f(t) = 2200 + 400t is constant and relative growth rate of t/20 g(t) = 400(2 )is constant. Step 2 Consider f(t) = 2200 + 400t The growth rate of f(t)is given by df d dt= (dt00+400t) = 400 Thus df= 400which is a constant. dt Hence growth rate of f(t) = 2200 + 400t is constant.