Question

What is the rate of change of the function described in the table? A) 12/5 b)5 c)25/2 d) 25

Answer 1

Answer:

All of the above (see explanation)

Explanation:

The y-values form a geometric sequence with a common ratio of 5 (answer choice b).

Usually "rate of change" is taken to mean ...

... rate of change = (change in y)/(change in x)

Between -1 and 0, the (average) rate of change is ...

... (1/2 -1/10)/(0 -(-1)) = 2/5

Between 0 and 1, the rate of change is ...

... (5/2 -1/2)/(1 - 0) = 2

Between 1 and 2, the rate of change is ...

... (25/2 -5/2)/(2 -1) = 10

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For an exponential relation such as this, the rate of change varies from as close to zero as you like to as near infinity as you like. Hence, at some point on the graph, the rate of change will be any of the listed values.

Answer 2

Answer:

b)5

Step-by-step explanation:

This table does not describe a linear relationship.  This is because the table does not have a constant rate of change; between the first two points, the function changes by

(1/2 - 1/10)/(0--1) = (5/10 - 1/10)/(1) = 5/10 - 1/10 = 4/10 = 2/5

Between the second two points, the function changes by

(5/2-1/2)/(1-0) = (4/2)/1 = 4/2 = 2

Comparing the first two y-coordinates, we have 1/10 and 1/2 = 5/10.  This is the result of multiplication by 5.

Comparing the second two y-coordinates, we have 1/2 and 5/2.  This is the result of multiplication by 5.

Comparing the rest of the y-coordinates, we can see that each time, the y-coordinate is multiplied by 5.  This means the rate of change is 5.