What is the slope of the graph?
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Answer:
For section A, the average rate of change is 12. For section B, the average rate of change is 300. The average rate of change in Section B is greater than Section A by 25. The rate of change keeps on increasing because the slope of the function is increasing.
Step-by-step explanation:
Concept: For a function f(x), the rate of change is given by . Given function is h(x) = 3(5∧x).
For x = 0 to x = 1, the value of function would be f(0) = 3 to f(1) = 15.
The rate of change would be (15-3) / (1-0) = 12.
For x = 2 to x = 3, the value of function would be f(2) = 75 to f(3) = 375.
The rate of change would be (375-75) / (3-2) = 300.
The average rate of change in Section B is greater than Section A by
300 / 12 = 25.
Looking at the function, that is h(x) = 3(5∧x), we see that this function is an increasing function. The slope of an increasing function keeps on increasing with the value of x. The rate of increase is also a slope. That is why the rate keeps on increasing.
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