Question

13 the function h(x) is used to calculate the average height, in 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 h(x) 6 12 24 51 60 64 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: Recall the average rate of change formula

The average rate of change of a function \( h(x) \) between \( x = a \) and \( x = b \) is given by \( \frac{h(b)-h(a)}{b - a} \).

Step2: Identify the values from the table

From the table, when \( x = 4 \), \( h(4)=12 \) and when \( x = 12 \), \( h(12) = 60 \). Here, \( a = 4 \), \( b=12 \), \( h(a)=12 \), \( h(b) = 60 \).

Step3: Calculate the average rate of change

Substitute the values into the formula: \( \frac{h(12)-h(4)}{12 - 4}=\frac{60 - 12}{8}=\frac{48}{8}=6 \).

Answer:

6