Does anybody know what the answer to this question is?

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and t

WINSTONCH [101]

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

$\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}$

Seperate the differential equation and solve for the constant C.

$\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}$

You have 100 rodents when:

$100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months$

You have 1000 rodents when:

$1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months$

7 0

3 years ago

If two angles are complementary angles and they measure m ∠1=(x + 5) and m∠2=(5x + 13). Find x and the measure for both an

Korolek [52]

5X+13+X+5=90°(SUM OF COMPLEMENTRY ANGLE IS EQUAL TO 90°)

6+18=90°

6X=90°-18°

X=72°/6

X=12 °ANSWER

6 0

3 years ago

2. At Fly-Right Airlines, passengers are informed that checked bags must weigh 40 lb or less, or they will have to pay a fee for

Ilya [14]

Answer:

see below

Step-by-step explanation:

a) w <= 40 lbs

b) Do you have any bag that weigh 0 lbs or negative lbs?

We need to rewrite the inequality so that these are not there

0<= w <= 40 lbs

6 0

3 years ago

At 88°F, a certain insect chirps at a rate of 64 times per minute, and at 97°F, they chirp 118 times per minute. Write an equati

Allushta [10]

Let " x " denotes the temperature in degree Fahrenheit .

Let " y " denotes the chirp rate per minute .

We have given that at 88 degree Fahrenheit , chirp rate is 64 times per minute and at 97 degree Fahrenheit , it is 118 times per minute .

We write this information in coordinate form ( x,y) .

We have ( x₁ ,y₁) = ( 88 , 64 ) and ( x₂ , y₂) = ( 97,118) .

y₂ - y ₁ 118 - 64 54

Slope , m = ---------------------- = --------------------- = -----------

x₂ - x₁ 97 - 88 9

Slope , m = 6 .

Equation of line in slope intercept form is

y = m x + b where ' m' is slope and ' b ' is intercept .

Plug value of m , we get

y = 6 x + b .

To find value of b , we put ( 88 , 64 ) in place of x and y .

Put x = 88 and y = 64 , we get

64 = 6 * 88 + b

64 = 528 + b

64 - 528 = b

- 464 = b

Thus we get b = - 464 .

So the equation become

y = 6 x - 464 .

Equation in slope intercept form representing the situation is

y = 6 x - 464 .

6 0

3 years ago

Should i do my teast for 12th grade calculus

Salsk061 [2.6K]

Answer:

attempt it, if it's too hard, sleep

that's what I would do lol

Step-by-step explanation:

3 0

3 years ago

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