Temperature AF
40 1000
60 1840
70 2260
85 2890
Find a linear model for the number of acre-feet of water that evaporate as function of temperature.
E(T)=
Is the answer E(T)=42T-960?
Substituting any one of the known values for temperature, does that give you the known value for evaporation?
To find a linear model for the number of acre-feet of water that evaporate as a function of temperature, we can use the given data points to calculate the slope and y-intercept of the linear equation.
Using the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, we can calculate the values.
Let's use the first two data points to find the slope:
m = (y2 - y1) / (x2 - x1)
= (1840 - 1000) / (60 - 40)
= 840 / 20
= 42
Now, let's use the slope and one of the data points (for example, 40, 1000) to find the y-intercept:
b = y - mx
= 1000 - (42 * 40)
= 1000 - 1680
= -680
So the linear model for the number of acre-feet of water that evaporates as a function of temperature is:
E(T) = 42T - 680
Therefore, the answer E(T) = 42T - 960 is incorrect.
To find the linear model for the number of acre-feet of water that evaporate as a function of temperature, you can use the given data points to calculate the slope and the y-intercept.
Let's calculate the slope first. The slope of a linear equation can be found using the formula:
Slope (m) = (Change in y) / (Change in x)
We can choose any two data points to calculate the slope. Let's pick the first two points: (40, 1000) and (60, 1840).
Change in y = 1840 - 1000 = 840
Change in x = 60 - 40 = 20
Slope (m) = 840 / 20 = 42
Now, let's calculate the y-intercept. The y-intercept is the value of y when x is equal to 0. We can use the equation of a line to find the y-intercept:
y = mx + b
where m is the slope and b is the y-intercept.
Using the first data point (40, 1000):
1000 = 42 * 40 + b
1000 = 1680 + b
b = 1000 - 1680
b = -680
Therefore, the y-intercept is -680.
Now we can write the linear model for the number of acre-feet of water evaporated (E(T)) as a function of temperature (T):
E(T) = 42T - 680
Therefore, the answer is E(T) = 42T - 680, not E(T) = 42T - 960.