Question

the function h(x) is used to calculate the average height, in inches, of a sunflower plant x weeks after it is transplanted. the data is represented in the table below:

x	2	4	6	9	12	16
h(x)	6	12	24	51	60	64

(1) between weeks 4 and 12, the average rate of change, in inches per week, is
(2) a
(3) 48
(4) 58

Explanation:

Step1: Identify values at x=4 and x=12

From the table, when \( x = 4 \), \( h(x)=12 \); when \( x = 12 \), \( h(x)=60 \).

Step2: Apply average rate of change formula

The formula for average rate of change is \( \frac{h(x_2)-h(x_1)}{x_2 - x_1} \). Here, \( x_1 = 4 \), \( x_2 = 12 \), \( h(x_1)=12 \), \( h(x_2)=60 \).
So, \( \frac{60 - 12}{12 - 4}=\frac{48}{8}=6 \). Wait, but the options given are (1)6, (2)8, (3)48, (4)56? Wait, maybe I misread the table. Wait, let's check again. Wait, maybe the x values: wait the table has x: 2,4,6,9,12,16? Wait no, the table as per the image: x values: 2,4,6,9,12,16? Wait the h(x) values: at x=2, h(x)=6; x=4, h(x)=12; x=6, h(x)=24; x=9, h(x)=51; x=12, h(x)=60; x=16, h(x)=64. Wait the question is between weeks 4 and 12. So x1=4, h(x1)=12; x2=12, h(x2)=60. Then average rate of change is (60 - 12)/(12 - 4)=48/8=6. So the answer should be 6, which is option (1).

Answer:

(1) 6