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(

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. 4. f(      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
# 4




Let's find the function value when x=1:


y=10%5Ex Start with the given equation.


y=10%5E%281%29 Plug in x=1.


y=10 Raise 10 to the first power to get 10


So if x=1, then y=10.

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Let's find the function value when x=2:


y=10%5Ex Start with the given equation.


y=10%5E%282%29 Plug in x=2.


y=100 Raise 10 to the second power to get 100


So if x=2, then y=100.

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Let's find the function value when x=4:


y=10%5Ex Start with the given equation.


y=10%5E%284%29 Plug in x=4.


y=10000 Raise 10 to the 4th power to get 10,000



So if x=4, then y=10000.

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Let's find the function value when x=8:


y=10%5Ex Start with the given equation.


y=10%5E%288%29 Plug in x=8.


y=100000000 Raise 10 to the 8th power to get 100,000,000


So if x=8, then y=100000000.

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Let's find the function value when x=16:


y=10%5Ex Start with the given equation.


y=10%5E%2816%29 Plug in x=16.


y=1%2A10%5E16 Raise 10 to the 16th power to get 1%2A10%5E16 (this is a 1 followed by 16 zeros)



So if x=16, then y=1%2A10%5E16.

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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.