Question

the table shows the average t - shirt prices in different years. ameena thinks that t - shirt prices have the greatest rate of change between 2005 - 2010. is she correct? explain your reasoning. she is correct; the rate of change between 2005 - 2010 is 0.194, and this is the greatest rate. she is incorrect; the rate of change between 2000 - 2005 is 0.212, and this is the greatest rate. she is incorrect; the rate of change between 2010 - 2015 is 0.250, and this is the greatest rate. she is incorrect; the rate of change between 2015 - 2020 is 0.172, and this is the greatest rate.

Explanation:

Step1: Calculate rate of change formula

The rate of change formula is $\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x$ represents the year and $y$ represents the price.

Step2: Calculate rate of change for 2000 - 2005

For 2000 - 2005: $x_1 = 2000,y_1=74.20,x_2 = 2005,y_2 = 75.26$.
Rate of change $=\frac{75.26 - 74.20}{2005 - 2000}=\frac{1.06}{5}=0.212$.

Step3: Calculate rate of change for 2005 - 2010

For 2005 - 2010: $x_1 = 2005,y_1=75.26,x_2 = 2010,y_2 = 76.23$.
Rate of change $=\frac{76.23 - 75.26}{2010 - 2005}=\frac{0.97}{5}=0.194$.

Step4: Calculate rate of change for 2010 - 2015

For 2010 - 2015: $x_1 = 2010,y_1=76.23,x_2 = 2015,y_2 = 77.17$.
Rate of change $=\frac{77.17 - 76.23}{2015 - 2010}=\frac{0.94}{5}=0.188$.

Step5: Calculate rate of change for 2015 - 2020

For 2015 - 2020: $x_1 = 2015,y_1=77.17,x_2 = 2020,y_2 = 78.03$.
Rate of change $=\frac{78.03 - 77.17}{2020 - 2015}=\frac{0.86}{5}=0.172$.

Answer:

She is incorrect; the rate of change between 2000 - 2005 is 0.212, and this is the greatest rate.