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pantera1 [17]
3 years ago
11

What is the average rate of change of the function g(x) = 3(2^x) - 6 over the interval [0,3]? Show all work.

Mathematics
1 answer:
slamgirl [31]3 years ago
6 0

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):

g(0)=3(2)^0-6

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):

g(3)=3(2)^3-6 so

g(3) = 18 and the coordinate pair is (3, 18).

Now we plug those into the slope formula:

m=\frac{18-(-3)}{3-0}=7

So the averagee rate of change, which is also the slope, between those 2 points is 7

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