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. (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.
I want the answers to d,e,f,g,h.
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.
(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.
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I want the answers to g,h.
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.
(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.
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