Chapter 8, Problem 29CR

To determine

To find: Whether the table of values represents a linear, exponential or a quadratic function then write the function.

Answer to Problem 29CR

It is exponential function.

  $y=128{(0.25)}^x$

Explanation of Solution

Given information: It is given that table of values (-1, 512), (0,128), (1,32),….

Formula used:

1. If first difference of y values are constant then it is linear
2. If second difference of y values are constant then it is quadratic
3. If ratio of$\frac{y_2}{y_1},\frac{y_3}{y_2}$ are constant then it is exponential.

Calculation:

The ratio of y values or difference of y values to find whether it is linear or exponential or quadratic.

Let’s try to find ratio of y values.

  $\frac{128}{512}=0.25$

  $\frac{32}{128}=0.25$

  $\frac{8}{32}=0.25$

Yes, the ratios of y values are constant. So, it is an exponential function.

Let’s find the function using formula $y=a{b}^x$

Here ‘ b’ is 0.25.

Initial value ‘ a’ is when x is 0, so, $a=128$

Plug in the values into the formula $y=128{(0.25)}^x$ .