Question

tell whether the rates of change are constant or variable. (example 1)

1. building measurements 2. computers sold
2. distance an object falls 4. cost of sweaters

Explanation:

Step1: Calculate rate of change for building measurements

Rate of change formula: $\frac{y_2 - y_1}{x_2 - x_1}$.
For first two points (3,1) and (12,4): $\frac{4 - 1}{12 - 3}=\frac{3}{9}=\frac{1}{3}$.
For second and third points (12,4) and (27,9): $\frac{9 - 4}{27 - 12}=\frac{5}{15}=\frac{1}{3}$.
For third and fourth points (27,9) and (75,25): $\frac{25 - 9}{75 - 27}=\frac{16}{48}=\frac{1}{3}$.

Step2: Calculate rate of change for computers sold

For first two points (2,6) and (4,12): $\frac{12 - 6}{4 - 2}=\frac{6}{2}=3$.
For second and third points (4,12) and (9,25): $\frac{25 - 12}{9 - 4}=\frac{13}{5}=2.6$.
Since $3
eq2.6$, rate is variable.

Step3: Calculate rate of change for distance an object falls

For first two points (1,16) and (2,64): $\frac{64 - 16}{2 - 1}=48$.
For second and third points (2,64) and (3,144): $\frac{144 - 64}{3 - 2}=80$.
Since $48
eq80$, rate is variable.

Step4: Calculate rate of change for cost of sweaters

For first two points (2,38) and (4,76): $\frac{76 - 38}{4 - 2}=\frac{38}{2}=19$.
For second and third points (4,76) and (7,133): $\frac{133 - 76}{7 - 4}=\frac{57}{3}=19$.
For third and fourth points (7,133) and (9,171): $\frac{171 - 133}{9 - 7}=\frac{38}{2}=19$.

Answer:

1. Constant
2. Variable
3. Variable
4. Constant