Marshall is comparing the growth rates of f(x)=6⋅1.5x and g(x)=5x+10 using this graph. Based on the graph, he concludes that the growth rate of g(x)=5x+10 is always greater than the growth rate of f(x)=6⋅1.5x. Where is his mistake?

Answer 1

Marshall's mistake is that he is comparing the y-values of two different functions at specific x-values on the graph, rather than comparing the growth rates overall. To accurately compare the growth rates, Marshall should compare the slopes of the two functions. The slope of g(x)=5x+10 is 5, while the slope of f(x)=6⋅1.5x changes depending on the value of x. Therefore, it is not accurate to conclude that the growth rate of g(x)=5x+10 is always greater than the growth rate of f(x)=6⋅1.5x.