the table represents the temperature of a cup of coffee over time. temperature of a cup of coffee\n| time…

the table represents the temperature of a cup of coffee over time. temperature of a cup of coffee\n| time (minutes) | temperature (degrees fahrenheit) |\n| ---- | ---- |\n| 0 | 200 |\n| 10 | 180 |\n| 20 | 163 |\n| 30 | 146 |\n| 40 | 131 |\n| 50 | 118 |\n| 60 | 107 |\nwhich model best represents the data set?\n- exponential, because there is a relatively consistent multiplicative rate of change\n- exponential, because there is a relatively consistent additive rate of change\n- linear, because there is a relatively consistent multiplicative rate of change\n- linear, because there is a relatively consistent additive rate of change

the table represents the temperature of a cup of coffee over time. temperature of a cup of coffee\n| time (minutes) | temperature (degrees fahrenheit) |\n| ---- | ---- |\n| 0 | 200 |\n| 10 | 180 |\n| 20 | 163 |\n| 30 | 146 |\n| 40 | 131 |\n| 50 | 118 |\n| 60 | 107 |\nwhich model best represents the data set?\n- exponential, because there is a relatively consistent multiplicative rate of change\n- exponential, because there is a relatively consistent additive rate of change\n- linear, because there is a relatively consistent multiplicative rate of change\n- linear, because there is a relatively consistent additive rate of change

Answer

Explanation:

Step1: Check additive rate of change

Calculate differences in temperature for equal - time intervals. From (t = 0) to (t = 10), (\Delta T=200 - 180 = 20). From (t = 10) to (t = 20), (\Delta T=180 - 163 = 17). Since the differences are not consistent, it is not linear with a consistent additive rate of change.

Step2: Check multiplicative rate of change

Calculate ratios of consecutive temperatures. (\frac{180}{200}=0.9), (\frac{163}{180}\approx0.906), (\frac{146}{163}\approx0.896), (\frac{131}{146}\approx0.897), (\frac{118}{131}\approx0.901), (\frac{107}{118}\approx0.907). The ratios are relatively consistent, indicating a multiplicative rate of change.

Answer:

exponential, because there is a relatively consistent multiplicative rate of change