SOLUTION: 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. 5.

Algebra ->  Graphs -> SOLUTION: 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. 5.       Log On


   

Question 156298: 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.


5. f(x) = ln x




Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

# 5

Note: ln(x) also looks like LN(x) (to pronounce it, simply read off the letters "L" "N")

This is the natural log of x. So it is a logarithmic function.

Let's find the y value when x=1


y=ln%28x%29 Start with the given equation.


y=ln%281%29 Plug in x=1.


y=0 Take the natural log of 1 to get 0


So when x=1, y=0.


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Let's find the y value when x=2


y=ln%28x%29 Start with the given equation.


y=ln%282%29 Plug in x=2.


y=0.693 Take the natural log of 2 to get 0.693


So when x=2, y=0.693.



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Let's find the y value when x=4


y=ln%28x%29 Start with the given equation.


y=ln%284%29 Plug in x=4.


y=1.386 Take the natural log of 4 to get 1.386


So when x=4, y=1.386.

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Let's find the y value when x=8


y=ln%28x%29 Start with the given equation.


y=ln%288%29 Plug in x=8.


y=2.079 Take the natural log of 8 to get 2.079


So when x=8, y=2.079.


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Let's find the y value when x=16


y=ln%28x%29 Start with the given equation.


y=ln%2816%29 Plug in x=16.


y=2.773 Take the natural log of 16 to get 2.773


So when x=16, y=2.773.


Now let's make a table of the values we just found.



Table of Values:





xy
10


20.693


41.386


82.079


162.773


Since the natural log function is logarithmic, this means that the growth is logarithmic. This growth rate is slower than linear growth rate and is the slowest growth rate than all of the growth rates.

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So here's the order of function's growth from smallest growth rate to largest growth rate

y=ln%28x%29, y=5x-3, y=x%5E2-3x%2B2, and y=2x%5E3%2B7x%5E2-x-1, and y=10%5Ex