SOLUTION: Hi
I'm confused with his question. However, my answer is below.
True or false: The function f(x)=3^x grows three times faster than the function g(x)=x. Explain.
MY answer is
Algebra.Com
Question 150404: Hi
I'm confused with his question. However, my answer is below.
True or false: The function f(x)=3^x grows three times faster than the function g(x)=x. Explain.
MY answer is true because F(x)=3^x is exponential and grows faster because what ever the x (exponent) is, it multiplies that 3, that many times over. And the g(x)=x is one number muliplied with another number. Is this correct or am I thinking of it the wrong way? Please help, I'm the only one who has this different answer and I don't understand why they all have false.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
True or false: The function f(x)=3^x grows three times faster than the function g(x)=x. Explain.
MY answer is true because F(x)=3^x is exponential and grows faster because what ever the x (exponent) is, it multiplies that 3, that many times over. And the
g(x)=x is one number multiplied with another number. Is this correct or am I thinking of it the wrong way? Please help, I'm the only one who has this different answer and I don't understand why they all have false.
----------------
Comparing g(x) = x to f(x)=3^x
g(x) = x is a line with slope=1 and y-intercept = 0
As x increases, y increases
It looks like this:
-----------------
y= 3^x is exponential with y-intercept at (0,1) and a constantly
increasing slope. It looks like this:
--------
Note: It is incorrect to say "the exponent multiplies the three".
-----------------
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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.
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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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