Question

The bar graph gives the average global temperature for eight selected years. a. Estimate the yearly increase in the average global temperature, rounded to the nearest hundredth of a degree.b. Write a mathematical model that estimates the average global temperature, T, in degrees Fahrenheit, x years after 1950.c. If the trend shown by the data continues, use your mathematical model from part (b) to project the average global temperature in .A bar graph titled "Average Global Temperature" has a horizontal axis and a vertical axis labeled "degrees Fahrenheit" from 56 to 59 in increments of 0.5. There are vertical bars, each of which is over a horizontal axis label. The heights of the bars are as follows, where the horizontal axis label is listed first and the height is listed second: 1950, 56.96; 1960, 57.05; 1970, 57.08; 1980, 57.31; 1990, 57.66; 2000, 57.69; 2010, 57.94; 2015, 58.31. Each bar is labeled with its height.Average Global Temperature1950196019701980199020002010201556575859degrees Fahrenheit56.9657.0557.0857.3157.6657.6957.9458.31Question content area bottomPart 1a. The yearly increase in the average global temperature is approximately   enter your response hereF per year.(Round to the nearest hundredth as needed.) Part 2b. A mathematical model that estimates the average global temperature, T, in degrees Fahrenheit, x years after 1950 is   enter your response here.(Use integers or decimals for any numbers in the expression. Use the answer from part (a) to find this answer.)Part 3c. The model from part (b) predicts the average global temperature will be   enter your response hereF in (Round to the nearest hundredth as needed. Use the answer from part (b) to find this answer.)

Answer 1

Step-by-step explanation:

a)

From the information given,

In 1950, average global temperature = 56.96

In 2015, average global temperature = 58.31

The values of the average temperature would be represented by y

The years would be represented by x

We want to calculate the average rate of change over the interval, 1950 to 2015

Average rate of change = (y2 - y1)/(x2 - x1)

x1 = 1950, y1 = 56.96

x2 = 2015, y2 = 58.31

Average rate of change or yearly increase = (58.31 - 56.96)/(2015 - 1950) = 1.35/65

yearly increase = 0.02F/year

b) We would write the mathematical model in the slope intercept form which is expressed as

y = mx + c

where

m = slope = 0.02

c is the y intercept. It is the value of y when x = 0. In this scenario, x = 0 is equivalent to 1950. The temperature in 1950 is 56.96. Thus, c = 56.96

The mathematical model would be

y = 0.02x + 56.96

where x represents the number of years after 1950

c) x = 2035 - 1950 = 85

By substituting x = 85 into the equation,

y = 0.02 * 85 + 56.96

y = 58.66

The average temperature in 2035 = 58.66 F