I really don't know how to do this, need as soon as possible. Please help!
A rabbit population satis es the logistic equation
dy
dt = 2x10^-7y(10^6- y);
where t is the time measured in months. The population is suddenly reduced to
40% of its steady state size by myxamatosis. If the myxamatosis then has no further effeect, how large is the population 8 months later? How long will it take
for the population to build up again to 90% of its steady state size?
thank you!
your equation is much too ambiguous .
How are x and y defined?
Is the exponent of 10 equal to -7 or is is it 10^(-7y) ?
what about the (10^6-y)?
Is that (10^6) - y , the way you typed it, or is it
10^(6-y)
sorry,
its 10 to the exponent -7 then y
and then (10 to the exponent 6 take y)
Find the slope of the line that passes through the points (–3, –6) and (1, 6).
A.
B.
C.
D.
13. Simplify
To solve this problem, we need to understand the behavior of the logistic equation and apply it to the given scenario. The logistic equation describes the growth of a population, taking into account factors such as limited resources and carrying capacity.
The logistic equation is given by:
dy/dt = k*y*(M - y)
Where:
- dy/dt represents the rate of change of the population size over time
- y represents the population size at a given time
- k is a constant that represents the growth rate
- M is the carrying capacity or the maximum population size that can be sustained
In this case, the logistic equation becomes:
dy/dt = 2*10^-7*y*(10^6 - y)
First, we are told that the population is suddenly reduced to 40% of its steady state size. The steady state size is the population size when there are no external influences affecting the growth. Therefore, we can set dy/dt equal to zero and solve for y to find the steady state size.
0 = 2*10^-7*y*(10^6 - y)
From here, we can solve for y. We can divide both sides of the equation by 2*10^-7*y to eliminate the factor from both sides:
0 = (10^6 - y)
Simplifying further, we get:
y = 10^6
So, the steady state size of the population is 1,000,000.
Now, the population is reduced to 40% of its steady state size, which means the new population size is 0.4 * 1,000,000 = 400,000.
Next, we need to determine how large the population will be 8 months later. For this, we need to solve the logistic equation using a numerical method called separation of variables or using a mathematical software.
Similarly, we need to determine how long it takes for the population to build up again to 90% of its steady state size. Again, we need to solve the logistic equation to determine the time required.
To obtain accurate solutions for these questions, it is best to use mathematical software or consult a mathematician to help with the calculations.