Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the time in hours. Interpret the following in practical terms, giving units. (a) f(2)= 3.0 O When t = 3.0, 2 cm of rain has fallen. When t = 2, 3.0 cm of rain has fallen. O 2 cm of rain fall at a rate of 3.0 cm per hour. O A total of 5 cm of rain falls on the ground. (b) f-¹(2.7) = 14 O When t = 2.7, then the rate of rainfall is 14 cm per hour. When 14 cm of rain have fallen, 2.7 hours have passed. When t = 14, then the rate of rainfall is 2.7 cm per hour. O When 2.7 cm of rain have fallen, 14 hours have passed. (c) f'(2) = 0.2 O At t = 0.2 hours, 2 cm of rain have accumulated. O When t = 2, the rate at which rain is falling is 0.2 cm per hour. At t = 2 hours, the rate of rainfall is 2 times as great as at t = 1. O When 0.2 hours have passed, the rate of rainfall is 2 cm per hour. (d) (f ¹) (2.7) = 9 O At t = 2.7 hours, the rain is falling at a rate of 9 cm per hour. When t = 2.7 hours, the rate of rainfall is increasing by 9 cm/hr² When 2.7 cm of rain have fallen, the rain is falling at a rate such that it will take 9 additional hours for another centimeter to fa O When t = 9 hours, the rate of rainfall is increasing by 2.7 cm/hr²
Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the time in hours. Interpret the following in practical terms, giving units. (a) f(2)= 3.0 O When t = 3.0, 2 cm of rain has fallen. When t = 2, 3.0 cm of rain has fallen. O 2 cm of rain fall at a rate of 3.0 cm per hour. O A total of 5 cm of rain falls on the ground. (b) f-¹(2.7) = 14 O When t = 2.7, then the rate of rainfall is 14 cm per hour. When 14 cm of rain have fallen, 2.7 hours have passed. When t = 14, then the rate of rainfall is 2.7 cm per hour. O When 2.7 cm of rain have fallen, 14 hours have passed. (c) f'(2) = 0.2 O At t = 0.2 hours, 2 cm of rain have accumulated. O When t = 2, the rate at which rain is falling is 0.2 cm per hour. At t = 2 hours, the rate of rainfall is 2 times as great as at t = 1. O When 0.2 hours have passed, the rate of rainfall is 2 cm per hour. (d) (f ¹) (2.7) = 9 O At t = 2.7 hours, the rain is falling at a rate of 9 cm per hour. When t = 2.7 hours, the rate of rainfall is increasing by 9 cm/hr² When 2.7 cm of rain have fallen, the rain is falling at a rate such that it will take 9 additional hours for another centimeter to fa O When t = 9 hours, the rate of rainfall is increasing by 2.7 cm/hr²
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the time in hours.
Interpret the following in practical terms, giving units.
(a) f(2)= 3.0
O When t = 3.0, 2 cm of rain has fallen.
O When t = 2, 3.0 cm of rain has fallen.
O 2 cm of rain fall at a rate of 3.0 cm per hour.
O A total of 5 cm of rain falls on the ground.
(b) f¹(2.7) = 14
O When t = 2.7, then the rate of rainfall is 14 cm per hour.
O When 14 cm of rain have fallen, 2.7 hours have passed.
O When t = 14, then the rate of rainfall is 2.7 cm per hour.
O When 2.7 cm of rain have fallen, 14 hours have passed.
(c) f'(2) = 0.2
O At t = 0.2 hours, 2 cm of rain have accumulated.
O When t = 2, the rate at which rain is falling is 0.2 cm per hour.
O At t = 2 hours, the rate of rainfall is 2 times as great as at t = 1.
O When 0.2 hours have passed, the rate of rainfall is 2 cm per hour.
(d) (f¹) '(2.7) = 9
O At t = 2.7 hours, the rain is falling at a rate of 9 cm per hour.
O When t = 2.7 hours, the rate of rainfall is increasing by 9 cm/hr²
O When 2.7 cm of rain have fallen, the rain is falling at a rate such that it will take 9 additional hours for another centimeter to fall.
O When t = 9 hours, the rate of rainfall is increasing by 2.7 cm/hr²
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