Question 5 The spread of a virus is modeled by V(t) = -t³ + t² + 12t, where V (t) is the number of people (in hundreds) with the virus and t is the number of weeks since the first case was observed. (a) Sketch V (t). (b) What is a reasonable domain of t for this problem? (c) Find the average rate of infection from t = 0 to t = 2. (d) Find the instantaneous rate of infection as a function of t using the limit definition of the derivative. (e) Find V(2) and V'(2). Write a sentence interpreting V(2) and V'(2) in terms of the number of infected people. Make sure to include units. (f) Sketch the tangent line to the graph you drew in a. at the point (2, V (2)). State the slope of the tangent line. (g) Use V(2) and V'(2) to estimate the value of V(2.1). (h) Find the maximum number of people infected at the same time and when the maximum occurs. Determine the rate of infection at this time.

Question 5 The spread of a virus is modeled by V(t) = -t³ + t² + 12t, where V (t) is the number of people (in hundreds) with the virus and t is the number of weeks since the first case was observed. (a) Sketch V (t). (b) What is a reasonable domain of t for this problem? (c) Find the average rate of infection from t = 0 to t = 2. (d) Find the instantaneous rate of infection as a function of t using the limit definition of the derivative. (e) Find V(2) and V'(2). Write a sentence interpreting V(2) and V'(2) in terms of the number of infected people. Make sure to include units. (f) Sketch the tangent line to the graph you drew in a. at the point (2, V (2)). State the slope of the tangent line. (g) Use V(2) and V'(2) to estimate the value of V(2.1). (h) Find the maximum number of people infected at the same time and when the maximum occurs. Determine the rate of infection at this time.

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.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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