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Hoochie [10]
3 years ago
9

I need help with number 4

Mathematics
1 answer:
Andrews [41]3 years ago
8 0
That one is really blurry
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The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,
uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right).

We need to solve it and obtain an expression for P(t) in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right).

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that k=0.04 and K=500 and the initial condition P(0)=100.

Notice that this equation is separable, then

\frac{dP}{P(1-P/K)} = kdt.

Now, intagrating in both sides of the equation

\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C.

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}.

So,

\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|.

We have obtained that:

-\ln\left| \frac{K-P}{P}\right| = kt +C

which is equivalent to

\ln\left| \frac{K-P}{P}\right|= -kt -C

Taking exponentials in both hands:

\left| \frac{K-P}{P}\right| = e^{-kt -C}

Hence,

\frac{K-P(t)}{P(t)} = Ae^{-kt}.

The next step is to substitute the given values in the statement of the problem:

\frac{500-P(t)}{P(t)} = Ae^{-0.04t}.

We calculate the value of A using the initial condition P(0)=100, substituting t=0:

\frac{500-100}{100} = A} and A=4.

So,

\frac{500-P(t)}{P(t)} = 4e^{-0.04t}.

Finally, as we want the value of t such that P(t)=200, we substitute this last value into the above equation. Thus,

\frac{500-200}{200} = 4e^{-0.04t}.

This is equivalent to \frac{3}{8} = e^{-0.04t}. Taking logarithms we get \ln\frac{3}{8} = -0.04t. Then,

t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325.

So, the population of rats will be 200 after 25 months.

6 0
3 years ago
Please help I’m confused
Amanda [17]

Answer:

First 3 boxes down are Vertical, Complementary, Supplementary . Second 3 Boxes Down Are add up to 90 degrees, add up to 180 degrees, and are congruent.

I hope this helps :)

5 0
2 years ago
Read 2 more answers
Solve x2 – 10x + 25 = 35 for x.
Galina-37 [17]

x^2-10x+25=35\\\\x^2-2\cdot5\cdot x + 5^2=35\ \ \ |\text{use:}\ (a-b)^2=a^2-2ab+b^2\\\\(x-5)^2=35\to x-5=\pm\sqrt{35}\ \ \ |+5\\\\\boxed{x=5-\sqrt{35}\ \vee\ x=5+\sqrt{35}}


\text{other method}\\\\x^2-10x+25=35\\\\x^2-5x-5x+25=35\\\\x(x-5)-5(x-5)=35\\\\(x-5)(x-5)=35\\\\(x-5)^2=35\\.....

3 0
3 years ago
Answer the following..
Greeley [361]

1. 25%

2. 24.5

3. 66.666666666667%

Have a good day! :)

8 0
3 years ago
Read 2 more answers
What is the domain of the function?<br> x + 3<br> f(x) =<br> VX + 3
ahrayia [7]

Your question is a little ambiguous, but I am assuming that you meant to say the function f(x) = x+3

Thus, I am solving your question based on assuming the function such as

f(x)=x+3

But, it would still clear your concept, no matter what the function is.

Answer:

we conclude that

\mathrm{Domain\:of\:}\:x+3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:

The graph is also attached.

Step-by-step explanation:

Given the function

f(x)=x+3

We know that the domain of a function is the set of input or argument values for which the function is real and defined.

As the function has no undefined points nor domain constraints.

Thus, the domain is

-\infty \:

Therefore, we conclude that

\mathrm{Domain\:of\:}\:x+3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:

The graph is also attached.

3 0
3 years ago
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