A given field mouse population satisfies the differential equation d⁢p/d⁢t=0.2p-390. where p is the number of...

A given field mouse population satisfies the differential equation

d⁢p/d⁢t=0.2p-390.

where p is the number of mice and t is the time in months.

(a) Find the time at which the population becomes extinct if

p(0)=1940⁢ .

Round your answer to two decimal places.

tf=

(c) Find the initial population p0 if the population is to become extinct in 1 year.

Round your answer to the nearest integer.

p0⁢=

Expert Solution

Colby Messinger answered 1 year ago

3. A population is modeled by the differential equation . (Obviously) For what values of P...

3. A population is modeled by the differential equation . (Obviously) For what values of P is the population increasing? Why?

Let c be a positive number. A differential equation of the form below where k is...

Let c be a positive number. A differential equation of the form below where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term ky1.01. If 4 such rabbits breed initially and the warren has 28 rabbits after three months, then when is doomsday? (Doomsday is the finite time t=T such that . Round...

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find...

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find the particular solution of the differential equation that satisfies the initial condition y(0) = 4 (c) What is the value of y when x = 1/2 2. (a) Find the general solution of the given differential equation: dy/dx = ysinx = ????? 2 (b) Find the particular solution of the differential equation that satisfies the initial condition ? = 2; ?ℎ?? ? = π/2

Find the particular solution of the first-order linear differential equation for x > 0 that satisfies...

Find the particular solution of the first-order linear differential equation for x > 0 that satisfies the initial condition. (Remember to use absolute values where appropriate.) Differential Equation Initial Condition x dy = (x + y + 7) dx y(1) = 6 y =

The consumer demand equation for tissues is given by q = (100 − p)2, where p...

The consumer demand equation for tissues is given by q = (100 − p)2, where p is the price per case of tissues and q is the demand in weekly sales. (a) Determine the price elasticity of demand E when the price is set at $34. (Round your answer to three decimal places.) E = Interpret your answer. The demand is going ? up down by % per 1% increase in price at that price level. (b) At what price should tissues...

For each of the following differential equations, find the particular solution that satisfies the additional given...

For each of the following differential equations, find the particular solution that satisfies the additional given property (called an initial condition). y'y = x + 1

1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation...

1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation and the initial condition f(1) = 12. 2.) An object moving on a line has a velocity given by v(t) = 3t^2 −4t+6. At time t = 1 the object’s position is s(1) = 2. Find s(t), the object’s position at any time t.

Write an equation in slope-intercept form of the line that satisfies the given conditions . Through...

Write an equation in slope-intercept form of the line that satisfies the given conditions . Through (-2,-2); parrallel to -x + 2y = 10

The number of snowplows needed by a town is given by s(p)=0.5p−0.01p^2. snowplows where p is...

The number of snowplows needed by a town is given by s(p)=0.5p−0.01p^2. snowplows where p is the population (in thousands). The projected population of the town t years from now is p(t)=150(1+12e^−0.02t)^-1 thousand people. (a) Write the model for the rate-of-change of the number of snowplows needed t years from now. (b) What will be the rate-of-change of the number of snowplows needed five years from now?

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A....

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A. dy/dx = y(xy^6 - 1) B. x dy/dx + y = 1/y^2 C. t^2 dy/dt + y^2 = ty

Question