Answer:
Explanation:
a. To write a linear function that describes the relationship between the electrical resistance R of a coil of wire and its temperature I, we need to determine the equation of a straight line that fits the given data points.
Using the data from the table, we can identify two points: (12, 5.05) and (32, 5.65). These points represent the temperature (in degrees Celsius) and the corresponding resistance (in milliohms) of the coil of wire.
Let's use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the given points.
Calculating the slope:
m = (5.65 - 5.05) / (32 - 12) = 0.6 / 20 = 0.03
Using the point-slope form with the first point (12, 5.05):
R - 5.05 = 0.03(I - 12)
Expanding and rearranging the equation:
R - 5.05 = 0.03I - 0.36
R = 0.03I - 0.36 + 5.05
Simplifying further:
R = 0.03I + 4.69
Therefore, the linear function R(I) that describes the relationship between the electrical resistance R of the coil of wire and its temperature I is R = 0.03I + 4.69.
b. To predict the resistance if the temperature of the coil of wire is 100° Celsius, we can substitute I = 100 into the linear function:
R = 0.03(100) + 4.69
R = 3 + 4.69
R = 7.69 milliohms
Therefore, if the temperature of the coil of wire is 100° Celsius, the predicted resistance is 7.69 milliohms.