Prices for emerald-shaped diamonds from an online trader are given in Table 2. Repeat Example 3 for this data with the linear model p = 5,600c – 1,100 where p is the price of an emerald-shaped diamond weighing c carats.

Table 2

Data from Example 3

Prices for round-shaped diamonds taken from an online trader are given in Table 1.

A linear model for the data in Table 1 is given by

where p is the price of a diamond weighing c carats. (We will discuss the source of models like this later in this section.) Plot the points in Table 1 on a Cartesian coordinate system, producing a scatter plot, and graph the model on the same axes.

Interpret the slope of the model in (2).

Use the model to estimate the cost of a 0.85-carat diamond and the cost of a 1.2-carat diamond. Round answers to the nearest dollar.

Use the model to estimate the weight of a diamond (to two decimal places) that sells for $4,000.

Transcribed Image Text:

Table 2 Emerald-Shaped Diamond Prices Weight (carats) 0.5 0.6 0.7 0.8 0.9 1.0 Price $1,677 $2,353 $2,718 $3,218 $3,982 $4,510