Question

Which of the following describes the function shown in the table below? x y -4 16 -1 2 2 0. 25 4 0. 0625 5 0. 03125 exponential, there is a constant rate of growth exponential, there is a constant rate of decay or decrease quadratic, there is a second degree change in the y-values quadratic, there is a constant difference between consecutive y-values.

Answer 1

The given table is an example of constant exponential decay.

It is given that

X          Y

-4          16

-1           2

2          0.25

4          0.0625

5          0.03125

What is an exponential function?

An exponential function is a relation of the form y = a^x, with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

The y-value at -4 is 16 while the y-value at -1 is 2, a decrement of 1/8 times for an increment in x-value by 3

Again, the y-value at 2 is 0.25 while the y-value at 5 is 0.03125, a decrement of 1/8 times for an increment in x-value by 3.

In both cases, the rate of decrement is constant.

So we can say that this is an example of constant exponential decay.

We can also see this behavior from the attached graph.

Therefore, the given table is an example of constant exponential decay.

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