- #1
dm59
- 5
- 0
dy/dt=(.5+sint)y/5 what is time t when the population has doubled?
sutupidmath said:[tex] \frac{dy}{dt}=\frac{(.5+sint)y}{5}[/tex] Well, you first need to solve this one, and come up with a function that predicts population at any point in time t. Do you know how to solve this diff, eq?
[tex] \frac{dy}{dt}=\frac{(.5+sint)y}{5}=>\frac{dy}{y}=\frac{1}{5}(.5+sint)dt[/tex]
Now integrate on both sides, and solve for y. I guess Y=f(t) or sth like that.
SO there is another info. that you have been provided with, Y(t)=2Yo, where Yo is your initial population. Have you been provided with initial population?or with another info. on this problem?
A differential equation is a mathematical equation that relates an unknown function to its derivatives. It is used to model various physical phenomena, such as population growth, and can be solved to determine the behavior of the function over time.
Population growth is the change in the number of individuals in a population over time. It can be affected by factors such as birth rate, death rate, immigration, and emigration.
Population growth is commonly modeled using the logistic differential equation, which takes into account the carrying capacity of the environment and the current population size. This equation can be solved to determine the growth rate and predict future population sizes.
Some common assumptions include a constant birth rate, a constant death rate, and a stable environment. However, these assumptions can be adjusted to better fit the specific population being studied.
Differential equations are commonly used in biology, ecology, and economics to model population growth and predict trends. They can also be applied to other areas, such as epidemiology, to study the spread of diseases within a population.