SOLUTION: Can someone explain this to me and show step by step so I can have a better understand of this problem thank you so much.
True or false: The function "f(x) = 3x" grows three tim
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Question 173173This question is from textbook
: Can someone explain this to me and show step by step so I can have a better understand of this problem thank you so much.
True or false: The function "f(x) = 3x" grows three times faster than the function "g(x) = x". Explain.
thank you so much
This question is from textbook
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming that the first function is
Think about it this way.
If , then and .
If , then and .
If , then and .
If , then and .
So we have this table of values
From the table, we can see that increments by 1 as x increments by 1. On the other hand, we can see that goes from 1 to 3 (a difference of 2), 3 to 9 (a difference of 6), 9 to 27 (a difference of 18), etc. So the differences between each term is: 2, 6, 18, etc....
This means that from x=0 to x=1, the average rate of change for g(x) is 2. From x=1 to x=2, the average rate of change for g(x) is 6. From x=2 to x=3, the average rate of change for f(x) is 18.
-------------------
So dividing the first average rate of change 2 by 1, we get . So from x=0 to x=1, is growing twice as fast as .
Dividing the second average rate of change 6 by 1, we get . So from x=1 to x=2, is growing six times as fast as .
Dividing the third average rate of change 18 by 1, we get . So from x=2 to x=3, is growing eighteen times as fast as .
As you can see, the exponential function is not growing at a constant rate. So cannot be growing 3 times faster than
Note: the function does however grow three times faster than , but that is for another problem.
So that means that the statement is false.
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