your friends height, for the first 10 years of their life, can be modeled with the function $h =…

your friends height, for the first 10 years of their life, can be modeled with the function $h = -0.2t^{2}+6.9t + 16$, where $t$ is the time in years since your friend was born and $h$ is the height in inches. what was the average rate of change, in inches per year, from year 2 to year 10? the average rate of change was $square$ inches per year.

your friends height, for the first 10 years of their life, can be modeled with the function $h = -0.2t^{2}+6.9t + 16$, where $t$ is the time in years since your friend was born and $h$ is the height in inches. what was the average rate of change, in inches per year, from year 2 to year 10? the average rate of change was $square$ inches per year.

Answer

Explanation:

Step1: Find height at (t = 2)

Substitute (t = 2) into (h=-0.2t^{2}+6.9t + 16). (h(2)=-0.2\times2^{2}+6.9\times2 + 16=-0.2\times4 + 13.8+16=-0.8+13.8 + 16=29)

Step2: Find height at (t = 10)

Substitute (t = 10) into (h=-0.2t^{2}+6.9t + 16). (h(10)=-0.2\times10^{2}+6.9\times10 + 16=-0.2\times100+69 + 16=-20+69+16=65)

Step3: Calculate average rate of change

The formula for average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 2), (b = 10), (f(t)=-0.2t^{2}+6.9t + 16). (\frac{h(10)-h(2)}{10 - 2}=\frac{65 - 29}{8}=\frac{36}{8}=4.5)

Answer:

(4.5)