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Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function ƒ¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).

Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function ƒ¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 3CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function f¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
Transcribed Image Text:Question The speed, V (km/h), of a car at time t (seconds) is given by. where 0 ≤t ≤ 150. 75 + 30sin (л(t-75) 150 V = f(t) 2- sin (π(t-75) 150 a) We want to know when the car will reach speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function f¯¹(t). b) Write down the domain of f¯¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f¯¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
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d) Describe the geometric relationship that you can see when you consider both f(t) and f-¹(t). e) When will the speed of the car be equal to 60km/h? Use the inverse function you found in part (a) to help you answer this.
Transcribed Image Text:d) Describe the geometric relationship that you can see when you consider both f(t) and f-¹(t). e) When will the speed of the car be equal to 60km/h? Use the inverse function you found in part (a) to help you answer this.
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This is Parts b and c of the same question.

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b) Write down the domain of f¨¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f-1(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
Transcribed Image Text:b) Write down the domain of f¨¹(t). c) Plot f(t) from t = 0 to t = 150 and then plot f-1(t) on the same axes but only for the values of t in the domain of the inverse function found in (b).
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