use the table to answer the question. x p(x)=sqrt(x)-5 q(x)=5sqrt3(x - 1) 0 -5 -5 1 -4 0 9 -2 10 compare the…

use the table to answer the question. x p(x)=sqrt(x)-5 q(x)=5sqrt3(x - 1) 0 -5 -5 1 -4 0 9 -2 10 compare the estimated average rates of change for the functions p(x)=sqrt(x)-5 and q(x)=5sqrt3(x - 1) over the interval 0.1,8.9. (1 point) the estimated average rates of change of p(x) and q(x) are both 1/3 over 0.1,8.9. the estimated average rates of change of p(x) and q(x) are both 5/3 over 0.1,8.9. the estimated average rate of change of q(x) is greater than the estimated average rate of change of p(x) over 0.1,8.9. the estimated average rate of change of q(x) is less than the estimated average rate of change of p(x) over 0.1,8.9.

use the table to answer the question. x p(x)=sqrt(x)-5 q(x)=5sqrt3(x - 1) 0 -5 -5 1 -4 0 9 -2 10 compare the estimated average rates of change for the functions p(x)=sqrt(x)-5 and q(x)=5sqrt3(x - 1) over the interval 0.1,8.9. (1 point) the estimated average rates of change of p(x) and q(x) are both 1/3 over 0.1,8.9. the estimated average rates of change of p(x) and q(x) are both 5/3 over 0.1,8.9. the estimated average rate of change of q(x) is greater than the estimated average rate of change of p(x) over 0.1,8.9. the estimated average rate of change of q(x) is less than the estimated average rate of change of p(x) over 0.1,8.9.

Answer

Answer:

The estimated average rate of change of (q(x)) is greater than the estimated average rate of change of (p(x)) over ([0.1,8.9]).

Explanation:

Step1: Fórmula de tasa de cambio promedio

La tasa de cambio promedio de una función (y = f(x)) en el intervalo ([a,b]) es (\frac{f(b)-f(a)}{b - a}).

Step2: Calcular tasa de cambio promedio de (p(x))

Para (p(x)=\sqrt{x}-5), (a = 0.1), (b=8.9). (p(0.1)=\sqrt{0.1}-5\approx - 4.68), (p(8.9)=\sqrt{8.9}-5\approx - 1.69). La tasa de cambio promedio es (\frac{p(8.9)-p(0.1)}{8.9 - 0.1}=\frac{(-1.69)-(-4.68)}{8.8}=\frac{2.99}{8.8}\approx0.34).

Step3: Calcular tasa de cambio promedio de (q(x))

Para (q(x)=5\sqrt[3]{x - 1}), (a = 0.1), (b = 8.9). (q(0.1)=5\sqrt[3]{0.1-1}=5\sqrt[3]{- 0.9}\approx - 4.85), (q(8.9)=5\sqrt[3]{8.9 - 1}=5\sqrt[3]{7.9}\approx10.37). La tasa de cambio promedio es (\frac{q(8.9)-q(0.1)}{8.9 - 0.1}=\frac{10.37-(-4.85)}{8.8}=\frac{15.22}{8.8}\approx1.73).

Step4: Comparar tasas de cambio

Como (1.73>0.34), la tasa de cambio promedio de (q(x)) es mayor que la de (p(x)) en el intervalo ([0.1,8.9]).