Question 188742: I'm having difficulty understanding this problem...
I am asked to evaluate the functions for the values of x given as 1,2,4,8 and 16. Describe the differences in the rate at which each function changes with increasing values of x:
if the functions are
f(x) = x^2 - 4x + 3 which is a quadratic function producing the points
(1,0)(2,-1),(4,3),(8,35),(16,195)
f(x) = 7^x which is an exponential function producing the points
(1,7)(2,49),(4,2401),(8,5764801), and (16,3.323X10^13)
f(x) = log x which is a logarithmic function producing the points
(1,0), (2,0.3), (4, 0.6), (8, 0.9)and (16, 1,2)
I am sure that the quadratic function is much more accelerated in rate than a linear function, and the exponential function is the fastest rate of all, with the slowest rate by the logarithmic function. But I am not sure how to justify each evaluation of rate? Could you please help me understand how to arrive at evaluating the differences in rate of these functions? Thanks!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You might do this. Pick the 1st and last point for each of
your examples. Find the slope for each of those cases. That
will give you the average slope over the interval. Compare
those averages.
You could also find the slope between each pair of points
and draw your conclusion.
Cheers,
Stan H.
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