Question

the table represents the temperature of a cup of coffee over time.

temperature of a cup of coffee
\

$$\begin{array}{|c|c|} \\hline \\text{time (minutes)} & \\text{temperature (degrees fahrenheit)} \\\\ \\hline 0 & 200 \\\\ \\hline 10 & 180 \\\\ \\hline 20 & 163 \\\\ \\hline 30 & 146 \\\\ \\hline 40 & 131 \\\\ \\hline 50 & 118 \\\\ \\hline 60 & 107 \\\\ \\hline \\end{array}$$

which model best represents the data set?

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

Explanation:

Analyze successive differences

$$
LATEXBLOCK0
$$

Analyze successive ratios

$$
LATEXBLOCK1
$$

Determine the best model

$$
LATEXBLOCK2
$$

Answer:

• exponential, because there is a relatively consistent multiplicative rate of change (Correct answer)
• exponential, because there is a relatively consistent additive rate of change
• linear, because there is a relatively consistent multiplicative rate of change
• linear, because there is a relatively consistent additive rate of change