Markin ! plz !
over the interval (13), the average rate of change of g is greater than the average rate of change of f.
as the value of x increases, the average rates of change of f and g (remain constant and constant and and and and increase) , respectively.
when the value of x is equal to 8, the value of (f(x) equals the value of g((x) exceeds value of f((x) exceeds value of g(x)
it can be further generalized that a quantity increasing exponentially will () exceed a quantity increasing linearly.

Step-by-step explanation:

a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).

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b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).

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c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:

  f(8) = 4·8 +3 = 35

  g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35

  g(8) > f(8)

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d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).

step-by-step explanation: