Question

The table below shows the weight of a child at their annual doctors appointment.

Number of households: 11 16 23 33 42 47
year: 2002 2003 2004 2005 2006 2007

for which interval was the average rate of change the smallest?
(1) 2002- 2004
(2) 2003 - 2005
(3) 2004 -2006
(4) 2005 - 2001

Answer 1

The correct answer is option 1. The smallest average rate of change of a child's weight occurred between the years 2002 and 2004, with an average increase of 6 pounds per year.

Step-by-step explanation:

The question pertains to the average rate of change in a child's weight over different year intervals. To find this, we use the formula for average rate of change, which is (change in weight)/(change in time). We compare these values for the intervals given: 2002-2004, 2003-2005, 2004-2006, and 2005-2007. Using the weight values from the provided table:

• For 2002-2004: (23 - 11) / (2004 - 2002) = 12/2 = 6 pounds per year
• For 2003-2005: (33 - 16) / (2005 - 2003) = 17/2 = 8.5 pounds per year
• For 2004-2006: (42 - 23) / (2006 - 2004) = 19/2 = 9.5 pounds per year
• For 2005-2007: (47 - 33) / (2007 - 2005) = 14/2 = 7 pounds per year

The smallest average rate of change was between the years 2002 and 2004, which is 6 pounds per year.