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Question 1: 259 11 12 (hours) L (t) 15 40 24 68 18 (cars per hour) The rate at which cars enter a parking lot is modeled by E(t) = 30 + 5(t – 2)(t – 5)e-02t The rate at which cars leave the parking lot is modeled by the differentiable function L. Selected values of L(t) are given in the table above. Both E (t) and L(t) are measured in cars per hour, and time t is measured in hours after 5 A.M. (t = 0). Both functions are defined for 0 < t < 12. a. What is the rate of change of E(t) at time t = 7? Indicate units of measure. b. How many cars enter the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole number. c. Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate " L(t)dt. Using correct units, explain the meaning of L(t)dt. d. For 0 st < 6,5 dollars are collected from each car entering the parking lot. For 6 < t s 12, 8 dollars are collected from each car entering the parking lot. How many dollars are collected from the cars entering the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole dollar.

Question 1: 259 11 12 (hours) L (t) 15 40 24 68 18 (cars per hour) The rate at which cars enter a parking lot is modeled by E(t) = 30 + 5(t – 2)(t – 5)e-02t The rate at which cars leave the parking lot is modeled by the differentiable function L. Selected values of L(t) are given in the table above. Both E (t) and L(t) are measured in cars per hour, and time t is measured in hours after 5 A.M. (t = 0). Both functions are defined for 0 < t < 12. a. What is the rate of change of E(t) at time t = 7? Indicate units of measure. b. How many cars enter the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole number. c. Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate " L(t)dt. Using correct units, explain the meaning of L(t)dt. d. For 0 st < 6,5 dollars are collected from each car entering the parking lot. For 6 < t s 12, 8 dollars are collected from each car entering the parking lot. How many dollars are collected from the cars entering the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole dollar.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 1: t 2 5 9 11 12 (hours) L (t) (cars per hour) 15 40 24 68 18 The rate at which cars enter a parking lot is modeled by E (t) = 30 + 5(t-2)(t-5)e-0.2t. The rate at which cars leave the parking lot is modeled by the differentiable function L. Selected values of L(t) are given in the table above. Both E (t) and L(t) are measured in cars per hour, and time t is measured in hours after 5 A.M. (t = 0). Both functions are defined for 0 ≤ t ≤ 12. a. What is the rate of change of E (t) at time t = 7? Indicate units of measure. b. How many cars enter the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole number. c. Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate ₂² L(t)dt. Using correct units, explain the meaning of ₂² L(t)dt. d. For 0 ≤ t < 6,5 dollars are collected from each car entering the parking lot. For 6 ≤ t ≤ 12, 8 dollars are collected from each car entering the parking lot. How many dollars are collected from the cars entering the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole dollar.
Transcribed Image Text:Question 1: t 2 5 9 11 12 (hours) L (t) (cars per hour) 15 40 24 68 18 The rate at which cars enter a parking lot is modeled by E (t) = 30 + 5(t-2)(t-5)e-0.2t. The rate at which cars leave the parking lot is modeled by the differentiable function L. Selected values of L(t) are given in the table above. Both E (t) and L(t) are measured in cars per hour, and time t is measured in hours after 5 A.M. (t = 0). Both functions are defined for 0 ≤ t ≤ 12. a. What is the rate of change of E (t) at time t = 7? Indicate units of measure. b. How many cars enter the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole number. c. Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate ₂² L(t)dt. Using correct units, explain the meaning of ₂² L(t)dt. d. For 0 ≤ t < 6,5 dollars are collected from each car entering the parking lot. For 6 ≤ t ≤ 12, 8 dollars are collected from each car entering the parking lot. How many dollars are collected from the cars entering the parking lot from time t = 0 to time t = 12? Give your answer to the nearest whole dollar.
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