Question

This list shows concentrations of carbon dioxide (in parts per million) in the Earth's atmosphere for the years 1950, 1955, 1960, 1965, 1970, 1975, 1980, and 1985. Find the mathematical model that best fits the data, and use it to predict the global mean temperature in 2015. Code 1950 as 1, 1955 as 2, and so on, in five-year segments.

311 314 317 320 326 331 339 346


A. linear model; 373

B. quadratic model; 412

C. exponential model; 374

D. power model; 346

Answer 1

Choice B

The mathematical model that best fits the data is a polynomial of order 2 as shown on the attachment.

The predicted global mean temperature in 2015 is; 412.24

Explanation:

The first step is to obtain a scatter plot of the data and then fit a trend line. A quadratic polynomial fits the data well considering the large value of the coefficient of determination of 0.9984.

To determine the global mean temperature in 2015 we substitute x with 14 in the quadratic model;

y = 0.4643(14)^2 + 0.7976 (14) + 310.07

= 412.24