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. 4. f(

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Question 156297: 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.

4. f(x) = 10^x



Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
# 4




Let's find the function value when :


Start with the given equation.


Plug in .


Raise 10 to the first power to get 10


So if , then .

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Let's find the function value when :


Start with the given equation.


Plug in .


Raise 10 to the second power to get 100


So if , then .

-------------

Let's find the function value when :


Start with the given equation.


Plug in .


Raise 10 to the 4th power to get 10,000



So if , then .

-------------

Let's find the function value when :


Start with the given equation.


Plug in .


Raise 10 to the 8th power to get 100,000,000


So if , then .

-------------

Let's find the function value when :


Start with the given equation.


Plug in .


Raise 10 to the 16th power to get (this is a 1 followed by 16 zeros)



So if , then .

-------------

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


Table of Values:





xy
110


2100


410,000


8100,000,000


161*10^16



Since we are dealing with an exponential function, this means that the function undergoes exponential growth. This is the fastest of all of the growth rates in this group.

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