Question

Compare the growth rate of the follow function using their graphs
f(x)=30x+300
and g(x)=300⋅(1.07)x
(Desmos Calculator).

According to the graph, which graph has a slower growth rate to start?

(1 point)
Responses

f(x)=30x+300
f of x is equal to 30 x plus 300

g(x)=300⋅(1.07)x

Answer 1

g(x) = 300·(1.07)^x grows more slowly at the start.

Reason: f(0)=g(0)=300, but f has constant slope 30 while g's initial rate is g'(0)=300·ln(1.07) ≈ 300·0.06766 ≈ 20.3, which is less than 30. Thus the exponential starts increasing more slowly than the line.