URGENT: magine that we are measuring rain fall with a rain gauge. After 1 hour of rain there is 1 inch of rain in the gauge. After 5 hours, there is 7 inches of rain in the gauge. Create a linear model to represent this situation, be sure to define your variable

T = 1 + 1.5x

Step-by-step explanation:

Based on the information provided and we can subtract the time and rain gauge at the end of the data with the time and rain gauge at the beginning. This tells us that in 4 hours the rain increased by 6 inches. If we divide these two values we get.

6 inches / 4 hours = 1.5 inches per hour

We now see that rain has been accumulating at a rate of 1.5 inches per hour. We can use this info to create a linear model where we multiply this rate by the number of hours that have passed (x) after 1 hour which would give us the total amount of rain (T)

T = 1 + 1.5x

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.