Question

the graph represents function h(t), which gives the height in inches of a bamboo plant t months after it has been planted. what is the value of h(11)? what is c if h(c) = 38? what is the value of? \\(\frac{h(14) - h(8)}{14 - 8}\\) what does this statement mean? \\(h(6) = 44\\)?

Explanation:

Step1: Find h(11) from graph

Locate t=11 on x-axis, find corresponding y-value: $h(11)=68$

Step2: Find c for h(c)=38

Locate y=38 on y-axis, find corresponding x-value: $c=5$

Step3: Calculate $\frac{h(14)-h(8)}{14-8}$

First find $h(14)=88$, $h(8)=48$. Substitute values:
$\frac{88-48}{14-8}=\frac{40}{6}=\frac{20}{3}\approx6.67$

Step4: Interpret h(6)=44

Translate function notation to real-world context.

Answer:

1. $h(11)=68$
2. $c=5$
3. $\frac{20}{3}$ (or approximately 6.67)
4. 6 months after being planted, the bamboo plant has a height of 44 inches.