Linear/ or Quadratic models

Question

Determine and explain which table of values represents a linear model, quadratic or neither. Use language such as differences and rate of change to provide a reasoning.

t H X Y r C

0 282.5 0 0.5 1 31.5

1 272.7 1 2 2 62.9

2 243.3 2 8 3 94.3

3 194.3 3 32 4 125.7

4 125.7 4 128 5 157.1

5 37.5

Answer 1

X Y is neither (there is a common ratio (4) between successive pairs of Y values so this is an exponential function)

r C approximately linear (difference between successive pairs of C values is approximately constant)

t H quadratic [ the second differences between successive pairs of H are approx constant]

First differences

-9.8 -29.4 -49 -68.6

Second differences

-19.6 -19,6 -19.6