Question

what does the average rate of change for temperature represent, measured as degrees per hour, between hour 0 and hour 5?
a \\( \frac { 1 } { 2 } \\) ; indicating the average temperature increases by 1 degree every 2 hours
b \\( \frac { 1 } { 2 } \\) ; indicating the average temperature increases by 2 degrees every 1 hour
c 2 ; indicating the average temperature increases by 2 degrees every 1 hour
d 2 ; indicating the average temperature increases by 1 degree every 2 hours

Explanation:

Step1: Calcular la pendiente (tasa de cambio)

La fórmula para la tasa de cambio promedio es $\frac{y_2 - y_1}{x_2 - x_1}$.
Supongamos que en $x = 0$ (hora 0), $y_1=20$ (grados) y en $x = 5$ (hora 5), $y_2 = 22.5$ (grados).
Entonces $\frac{y_2 - y_1}{x_2 - x_1}=\frac{22.5 - 20}{5 - 0}=\frac{2.5}{5}=\frac{1}{2}$.

Step2: Interpretar la tasa de cambio

La tasa de cambio $\frac{1}{2}$ significa que por cada 2 horas (denominador), la temperatura aumenta 1 grado (numerador).

Answer:

A. $\frac{1}{2}$; indicating the average temperature increases by 1 degree every 2 hours