Question

Consider the functions f and g below. f(x)=x+4 g(x)=(5/4)^x
Based on the graph of the functions, which of the following statements is true? Over the interval [3, 5], the average rate of change of g is greater than the average rate of change of f.
g(x) eventually exceeds f(x) because g(x) is increasing exponentially
f(x) eventually exceeds g(x) because f(x) is increasing linearly
At x = 13, the value of f(x) is more than the value of g(x).
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Answer 1

The second statement.

Any increasing exponential function will always eventually be greater than any other non-exponential function.

Answer 2

Answer:

g(x) eventually exceeds f(x) because g(x) is increasing exponentially

Step-by-step explanation:

Consider the functions f and g below. f(x)=x+4 g(x)=(5/4)^x

f(x) =x+4 is a linear function

g(x)= (5/4)^x is an exponential function

Exponential function increases rapidly as x increases

Linear function increases at a constant rate

The graph of exponential function exceeds the graph of linear and quadratic functions.

So ,  g(x) eventually exceeds f(x) because g(x) is increasing exponentially