The population of a virus in a host can be modeled by the function W that satisfies the differential equation dW dt = t - W₁ where W is measured in millions of virus cells and t is measured in days for 7 ≤ t < 12. At time t = 7 days, there are 14 million cells of the virus in the host. a) Write an equation for the line tangent to the graph of W at t = 7. Use the tangent line to approximate the number of virus cells in the host, in millions, at 10 days.

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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The population of a virus in a host can be
modeled by the function W that satisfies the differential equation
dW
dt
t - W
where W is measured in millions of virus cells and t is measured in days for
7<t< 12. At time t = 7 days, there are 14 million cells of the virus in the host.
a) Write an equation for the line tangent to the graph of W at t = 7. Use the
tangent line to approximate the number of virus cells in the host, in millions, at
10 days.
b) The host receives an antiviral medication. The amount of medication in the host is
modeled by the function A which satisfies the differential equation
dA
dt
1
-
(4), where A is measured in milligrams, t is measured in days since
2 t+b
the host received the medication, and b is a positive constant. If the amount of
medication in the host is 40 milligrams at time O days and 20 milligrams at time
9 days, what is A(t) in terms of t?
Transcribed Image Text:The population of a virus in a host can be modeled by the function W that satisfies the differential equation dW dt t - W where W is measured in millions of virus cells and t is measured in days for 7<t< 12. At time t = 7 days, there are 14 million cells of the virus in the host. a) Write an equation for the line tangent to the graph of W at t = 7. Use the tangent line to approximate the number of virus cells in the host, in millions, at 10 days. b) The host receives an antiviral medication. The amount of medication in the host is modeled by the function A which satisfies the differential equation dA dt 1 - (4), where A is measured in milligrams, t is measured in days since 2 t+b the host received the medication, and b is a positive constant. If the amount of medication in the host is 40 milligrams at time O days and 20 milligrams at time 9 days, what is A(t) in terms of t?
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