Chapter 8, Problem 14CT

To determine

To find: Whether the given table represents linear or exponential or quadratic and write the function.

Answer to Problem 14CT

It is linear function.

The function that models the data is $d=19t$

Explanation of Solution

Given information: It is given that the points (1, 19), (2, 38), (3,57), (4,76) and (5,95)

Calculation:

Let’s find the difference of x and y values to find whether it is linear or quadratic.

Time, t	Distance, d	First difference
1	19
2	38	19
3	57	19
4	76	19
5	95	19

The first difference of‘d’ is constant 19. So, it is a linear function.

Let’s find the linear rule like $y=mx+b$

Where ‘m’ is slope. From the table $m=19$

Plug in this value into the equation, it gives $y=19x+b$ .

Use one point to find the value of b.

Use (2, 38)

  $38=19(2)+b$

  $38=38+b$

Subtract both sides 38

  $b=0$

Now, plug in this value of b into $y=19x+b$ , it gives $y=19x+0$

Simplify it, it gives $y=19x\Rightarrow d=19t$