Chapter 6.3, Problem 27E

To determine

To find:Ordered pairs represent linear or exponential function.

Answer to Problem 27E

Ordered pairs matched with linear or exponential function.

Explanation of Solution

Given information :

  $m$ is an integer & $n\ne 0$ .

Concept used:

Use patterns between consecutive data pairs to determine type of function.

Linear function: - The difference of consecutive y-values is constant.

Consecutive ‘y’ values have a common ratio and they do not change by a constant amount.

Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

Consecutive y values change by a constant ratio.

Given ordered pairs

  $m,n$

Here $m$ increase by $1$ unit, $n$ increase by some unit. So, function is linear.

  $m+1,2n$

As you observe here the first coordinates of each ordered pair increases by $1$ whereas the second coordinates of each ordered pair are increased by a factor of $2$ . So, the ordered pair represents an exponential function.

  $m+2,4n$

As you observe here the first coordinates of each ordered pair increases by $2$ whereas the second coordinates of each ordered pair are increased by a factor of $4$ . So, the ordered pair represents an exponential function.

  $m+3,8n$

As you observe here the first coordinates of each ordered pair increases by $3$ whereas the second coordinates of each ordered pair are increased by a factor of $8$ . So, the ordered pair represents an exponential function.

  $m+4,16n$

As you observe here the first coordinates of each ordered pair increases by $4$ whereas the second coordinates of each ordered pair are increased by a factor of $16$ . So, the ordered pair represents an exponential function.

Hence,

Ordered pairs matched with linear or exponential function.