Use 2 facts to form 2 data points: (0, 48) and (100, 77) . You should find slope = m = 0.29 and b = 48 . So the linear equation to model the situation: y = 0.29x + 48

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.

t hope this

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