What is the average rate of change of the function g(x) = 3(2^x) - 6 over the interval [0,3]? Show all work.
1 answer:
Answer:
7
Step-by-step explanation:
The average rate of change here, since this is not a line, is the slope of the secant line that is connecting those 2 points. We can find that average rate of change by finding the y coordinates that go with each of those x coordinates and then applying the slope formula. For g(0):
Anything raised to the power of 0 is 1, so we have then:
g(0) = 3(1) - 6 so
g(0) = -3 and the coordinate pair is (0, -3)
For g(3):
so
g(3) = 18 and the coordinate pair is (3, 18).
Now we plug those into the slope formula:
So the averagee rate of change, which is also the slope, between those 2 points is 7
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The value of correlation coefficient (r) for the dataset is 0.981
<h3>What is correlation coefficient (r)?</h3>The correlation coefficient (r) is used to determine the closeness and association of a scatter plot points.
The dataset is given as:
- x: 8 15 3 7 2 14
- y: 15 21 6 12 3 20
Using a graphing calculator, we have the following parameters:
<h3>X Values </h3>- ∑x = 49
- Mean = 8.167
- ∑(X - Mx)2 = SSx = 146.833
<h3>Y Values </h3>
- ∑y = 77
- Mean = 12.833
- ∑(Y - My)2 = SSy = 266.833
<h3>X and Y Combined </h3>
- N = 6
- ∑(X - Mx)(Y - My) = 194.167
The correlation coefficient (r) is then calculated as:
This gives
Approximate
Hence, the value of correlation coefficient (r) for the dataset is 0.981
Read more about correlation coefficient at:
Answer:
Step-by-step explanation:
apply the inverse properties of logarithmic and exponential functions to simplify
all logs has base 'e'
Inverse property of log says that
, the value of ln e=1
we apply this property in our problem. ln has same base 'e' . ln and 'e' gets cancelled