In 1870 the average ground temperature in Paris was 11.8°C. Since then it has risen at a nearly constant rate, reaching 13.5°C in 1969.
(a) Express the temperature T (in °C) in terms of time t (in years), where t = 0 corresponds to the year 1870 and 0 ≤ t ≤ 99. (Give your answer in slope-intercept form.)
(b) During what year was the average ground temperature 12.7°C?
T = {[(13.5 - 11.8) / 99] * t } + 11.8
plug in 12.7 for T , and solve for t
gg
(a) To express the temperature T in terms of time t, we can use the equation of a straight line, which is given by y = mx + b, where m is the slope and b is the y-intercept.
In this case, we are given two points: (0, 11.8) and (99, 13.5).
First, we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (13.5 - 11.8) / (99 - 0)
m = 1.7 / 99
m ≈ 0.0172
Next, we can substitute one of the points (0, 11.8) into the equation y = mx + b and solve for the y-intercept (b).
11.8 = 0.0172(0) + b
11.8 = b
Therefore, the equation in slope-intercept form for the temperature T in terms of time t is:
T = 0.0172t + 11.8
(b) To find the year when the average ground temperature was 12.7°C, we need to substitute 12.7 for T in the equation above and solve for t.
12.7 = 0.0172t + 11.8
Subtracting 11.8 from both sides:
0.9 = 0.0172t
Dividing both sides by 0.0172:
t ≈ 52.33
The closest whole number to 52.33 is 52. So the average ground temperature of 12.7°C occurred in the year 1870 + 52 = 1922.