dark_knight_307
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- Feb 9, 2008
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I have an issue with the following Calculus problems; I have no idea how to do them. Here they are....
At time t=0, a bacterial culture weighs 1 gram. Two hours later, the culture weighs 2 grams. The maximum weight of the culture is 10 grams.
1. Write a non-differential logistics equation that models the weight of the bacterial culture. Be sure to define each constant and the variables in terms of this problem.
2. Find the culture's weight after 5 hours.
3. When will the culture's weight reach 8 grams?
4. Write a logistics differential equation that models the growth rate of the culture's weight. Then repeat parts 2. and 3. using Euler's Method with a step size of h=1. Compare the approximation with the exact answers.
5. At what time is the culture's weight increasing most rapidly?
Also, if anyone can help me integrate the following first order differential equation, I'd appreciate it!...
dy=(y(tan x) + 2e^x)dx
I got it this far....
y = (C/abs(cos x))*(integral of e^x*abs(cos x)*dx)
And here's another one....
An object falling near the earth's surface encounters air resistance that is proportional to its velocity. The acceleration due to gravity is -9.8m/s^2. So, without air resistance the object's acceleration can be modeled by the differential equation. dv/dt = -9.8. But aerodynamic drag represents a considerable retarding force as velocity increases. Thus a better model for an object falling near the surface of the earth is: dv/dt = kv - 9.8, where k is a constant of proportionality.
1. What are the units of k? Is k positive or negative?
2. Find the velocity of the object as a function of time if the initial velocity is V sub 0.
3. Use #2 to find the limit of the velocity as t -> infinity.
4. Find the position function s(t) of the object.
At time t=0, a bacterial culture weighs 1 gram. Two hours later, the culture weighs 2 grams. The maximum weight of the culture is 10 grams.
1. Write a non-differential logistics equation that models the weight of the bacterial culture. Be sure to define each constant and the variables in terms of this problem.
2. Find the culture's weight after 5 hours.
3. When will the culture's weight reach 8 grams?
4. Write a logistics differential equation that models the growth rate of the culture's weight. Then repeat parts 2. and 3. using Euler's Method with a step size of h=1. Compare the approximation with the exact answers.
5. At what time is the culture's weight increasing most rapidly?
Also, if anyone can help me integrate the following first order differential equation, I'd appreciate it!...
dy=(y(tan x) + 2e^x)dx
I got it this far....
y = (C/abs(cos x))*(integral of e^x*abs(cos x)*dx)
And here's another one....
An object falling near the earth's surface encounters air resistance that is proportional to its velocity. The acceleration due to gravity is -9.8m/s^2. So, without air resistance the object's acceleration can be modeled by the differential equation. dv/dt = -9.8. But aerodynamic drag represents a considerable retarding force as velocity increases. Thus a better model for an object falling near the surface of the earth is: dv/dt = kv - 9.8, where k is a constant of proportionality.
1. What are the units of k? Is k positive or negative?
2. Find the velocity of the object as a function of time if the initial velocity is V sub 0.
3. Use #2 to find the limit of the velocity as t -> infinity.
4. Find the position function s(t) of the object.