Question

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

( x )	2	4	6	9	12	16

between weeks 4 and 12, the average rate of change, in inches per week, is
(1) 6
(2) 8
(3) 48
(4) 58

Explanation:

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

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

Step2: Apply average rate of change formula

The formula for average rate of change between \( x = a \) and \( x = b \) is \( \frac{h(b)-h(a)}{b - a} \). Here, \( a = 4 \), \( b = 12 \), so:

$$ \frac{h(12)-h(4)}{12 - 4}=\frac{60 - 12}{8}=\frac{48}{8}=6 $$

Answer:

(1) 6