Question 153160: Hi
How would I solve the following: Exponent and logarithm as function of power
True or false: The function "f(x) = 3x" grows three times faster than the function "g(x) = x". Explain. I got two different answer when I tried to solve this logarithm. Can you please help me.
Answer: False.
If x = 3 it would make f(3)=3 * 3 =9 and g(3)=3
If x = 4 then f(4)=12 and g(4)=4
if x=5 then f(5)=15 and g(5)=5
although f(x) is 3 times greater than g(x) the growth of f(x) is not 3 times faster than g(x) because from 9 the change of f(x) is only 3 and from 12 it only changed by 3 again. wherein it should have incurred a change of 9. If f(x) grows three times faster than g(x) the equation should be f(x)=x raise to the 3rd power and g(x)=x.
Answer is True
The question is on rate of growth, ie slope.
slope of g(x) is 1.
slope of f(x) is 3.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1st: This is not a logarithm problem
2nd: When you say " it should have grown by 9 " you are
pointing to the fact that when x increased from 0 to 3
f(x) increased from 0 to 9.
That is true.
But, if x had increased from 0 to 1 f(x) would have increased
by only 3. Similarly for x increasing from 1 to 2, then from
2, to 3. So for each increase in x by one f(x) increases by 3.
That is a description of the slope; and the slope is the rate
of growth for a linear function.
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Cheers,
Stan H.
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