Question 173795: I am having trouble getting these two. Can someone please help me...please..Thank you..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.
3.f(x) = 2x3 + 7x2 - x - 1
5.f(x) = ln x
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! To evaluate a function, such as  , at a given value of the independent variable, substitute the value for every instance of the variable in the function and then do the appropriate arithmetic.
In general, if then  .
Specifically: if then 
All you need to do is the arithmetic, and then make the other substitutions/do the arithmetic for the other given values.
For  , just use your Windows built in calculator in Scientific mode. Enter the number to be substituted for  and then click the 'ln' key. Writing down two or three decimal places should be plenty. For example,  is approximately equal to 0.69314718055994530941723212145818 according to the Windows calculator, but an answer of 0.69 or 0.693 is probably good enough unless your instructor told to you respond with greater precision for some reason.
As to the rate of change of the function as the independent variable increases, your first function changes very fast except in the area of the local minimum and local maximum near the zeros of the function.  always gets larger as increases, but at a much slower rate. See below for a graph of the two functions, is the green one:
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