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.
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.
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 14TI: The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14...
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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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