Question

at the beginning of each year, annie stepped on her scale and resolved to become more fit.
annies weight
according to the table, when was the rate of decrease greater?
between 2012 and 2015
between 2013 and 2016

Explanation:

Step1: Calculate the rate of decrease between 2012 and 2015

The formula for the rate of decrease is \(\frac{\text{Initial Value}-\text{Final Value}}{\text{Initial Value}}\).
For 2012 - 2015:
Initial value \(= 235\) kg, final value \(= 217\) kg.
The decrease amount \(=235 - 217=18\) kg.
The rate of decrease \(r_1=\frac{235 - 217}{235}=\frac{18}{235}\approx0.0766\)

Step2: Calculate the rate of decrease between 2013 and 2016

For 2013 - 2016:
Initial value \(= 262\) kg, final value \(= 238\) kg.
The decrease amount \(=262-238 = 24\) kg.
The rate of decrease \(r_2=\frac{262-238}{262}=\frac{24}{262}\approx0.0916\)

Step3: Compare the two rates

Since \(0.0916>0.0766\) (i.e., \(r_2 > r_1\))

Answer:

between 2013 and 2016