find the value of the given function at each end of the range of values of the variable. then, calculate the…

find the value of the given function at each end of the range of values of the variable. then, calculate the average rate of change of the function between the two values of the variable. t(x) = √(x - 9)/4 ; 9 ≤ x ≤ 18 t(9) = (type an integer or decimal rounded to the nearest thousandth as needed.) t(18) = (type an integer or decimal rounded to the nearest thousandth as needed.) the average rate of change of t(x) from 9 to 18 is (type an integer or decimal rounded to the nearest thousandth as needed.)

find the value of the given function at each end of the range of values of the variable. then, calculate the average rate of change of the function between the two values of the variable. t(x) = √(x - 9)/4 ; 9 ≤ x ≤ 18 t(9) = (type an integer or decimal rounded to the nearest thousandth as needed.) t(18) = (type an integer or decimal rounded to the nearest thousandth as needed.) the average rate of change of t(x) from 9 to 18 is (type an integer or decimal rounded to the nearest thousandth as needed.)

Answer

Explanation:

Step1: Calcular t(9)

Sustituir x = 9 en t(x): [t(9)=\sqrt{\frac{9 - 9}{4}}=\sqrt{0}=0]

Step2: Calcular t(18)

Sustituir x = 18 en t(x): [t(18)=\sqrt{\frac{18 - 9}{4}}=\sqrt{\frac{9}{4}}=\frac{3}{2}=1.5]

Step3: Calcular la tasa media de cambio

La fórmula para la tasa media de cambio de una función (y = t(x)) de (x=a) a (x = b) es (\frac{t(b)-t(a)}{b - a}). Aquí, (a = 9), (b = 18), (t(9)=0) y (t(18)=1.5). [\frac{t(18)-t(9)}{18 - 9}=\frac{1.5-0}{9}=\frac{1.5}{9}\approx0.167]

Answer:

t(9) = 0 t(18) = 1.5 La tasa media de cambio de t(x) de 9 a 18 es 0.167