the logistic differential equation models the growth rate of a population. use the equation to find the value of k, find the carrying capacity, use a computer algebra system to graph a slope field, and determine the value of P at which the population growth rate is the greatest.   the differential equation is : dP/dt = 0.1P - 0.0004 P2

Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. The growth parameter for this type of fish is r = 3.0. The logistic growth formula is given by PN+1 rPN(1-PN) If originally the pond is stocked to 50% of its carrying capacity, then the population of the pond after the second breeding season is Select one: a. 25% of the pond's carrying capacity. b. 56.25% of the pond's carrying capacity. c. 75% of the pond's carrying capacity. d. none of these O e. 50% of the pond's carrying capacity.

A material has an initial of 15 units. Which equation models the amount of the material y, decaying exponentially at a rate of 23% over time x

Newton's law of cooling relates the rate at which a body cools to the difference in temperature between the body and the environment into which it is introduced. The formula is F(t) = To + Cb¹, where F(t) is the temperature of the body at time t, To is the constant temperature of the environment into which the body is introduced, and C and b are constants. Use Newton's law of cooling to solve the problem below. A cup of coffee has cooled from 98° to 50° after 15 minutes in a room at 23°. How long will it take to cool to 30°? It will take approximately minutes. (Round to the nearest integer as needed.) (...)