The rate of change of the population of a small town is dP/dt = kP
The rate of change of the population of a small town is dP/dt = kP, where P is the population, t is time in years and k is the growth rate.
If P = 20000 when t = 3 and P = 30000 when t = 4, what is the population when t= 10?
Round your answer to the nearest integer.
Homework Answers
Suppose that the rate of change of a population is given by: dP dt = kP(M-P) a) What model of pop...
Suppose that the rate of change of a population is given by: dP dt = kP(M-P) a) What model of population growth is this ? b) What does it predict for the growth of the population as the population increases ? c) Sketch what happens to the population if the initial population, Po, were such that G) 0< Po< M/2, (ii) M/2 < PoM and (iii) Po > M (all on the same graph of population as a function of...
The rate of growth dP/dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 8
The rate of growth dP/dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 8, where P is the population size and t is the time in days (0≤ t ≤ 10). The initial size of the population is 200. Approximate the population after 7 days. Round the answer to the nearest integer.
POPULATION MODELS: PLEASE ANSWSER ASAP: ALL 3 AND WILL RATE U ASAP. The logistic growth model...
POPULATION MODELS: PLEASE
ANSWSER ASAP: ALL 3 AND WILL RATE U ASAP.
The logistic growth model describes population growth when
resources are constrained. It
is an extension to the exponential growth model that includes an
additional term introducing
the carrying capacity of the habitat.
The differential equation for this model is:
dP/dt=kP(t)(1-P(t)/M)
Where P(t) is the population (or population density) at time t,
k > 0 is a growth constant,
and M is the carrying capacity of the habitat. This...
Part B Please!! Scenario The population of fish in a fishery has a growth rate that...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
Logistic Population Growth
I do not understand how to work this type of problem. The logistic growth model is dP/dt = kP(1-P/M) or dP/dt = (k/M)P(M-P) where P is population, k is aconstant growth rate and M is the carrying capacity. The question I'm having trouble with is dP/dt = 0.04P - 0.0004P^2 and I am supposed to find k and M, I have noidea where to even start
Question Details The population of a town grows at a rate proportional to the population present...
Question Details The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 in by 10% in 10 years, what will be the population in 50 years? (Round your answer to the nearest person.) persons How fast is the population growing at t-50? (Round your answer to two decimal places.) persons/yr + Ask Yc Question Details
9. The population of a small town in Montana in 1985 was found to be given...
9. The population of a small town in Montana in 1985 was found to be given by P = 30,000e" where t is time measured from 1985. a. What was the population in the year 2000? b. When will the population of that town reach 90,000. 9. The population of a small town in Montana in 1985 was found to be given by P = 30,000.025 where t is time measured from 1985. a. What was the population in the...
Suppose that a population of hacteria grows according to the logistic differential equation dP =0.01P-0.0002P2 dt...
Suppose that a population of hacteria grows according to the logistic differential equation dP =0.01P-0.0002P2 dt where Pis the population measured in thousands and t is time measured in days. Logistic growth differential equations are often quite difficult to solve. Instead, you will analyze its direction field to acquire infom ation about the solutions to this differential equation. a) Calculate the maximum population M that the sumounding environment can austain. (Note this is also calked the "canying capacity"). Hint: Rewrite...
(1 point) Any population, P, for which we can ignore immigration, satisfies dP Birth rate –...
(1 point) Any population, P, for which we can ignore immigration, satisfies dP Birth rate – Death rate. dt For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the form dP аP? — ЬР with a, b > 0. dt This problem investigates the solutions to...
The population of fish, P, in a lake is a function of time, t, measured in years. The rate of cha...
The population of fish, P, in a lake is a function of time, t, measured in years. The rate of change of P is given by 7600e0.4t fish/year. dt(19 + e0.4t)2 dp dt a. Graph on the domain [0, 20]. Make sure your graph is properly labeled. b. Estimate the change in population on the time interval 0 s t š 20 years. Use 10 intervals, each lasting two years. Use rate of change data from the left side of...
Suppose that the rate of change of a population is given by: dP dt = kP(M-P) a) What model of population growth is this ? b) What does it predict for the growth of the population as the population increases ? c) Sketch what happens to the population if the initial population, Po, were such that G) 0< Po< M/2, (ii) M/2 < PoM and (iii) Po > M (all on the same graph of population as a function of...
POPULATION MODELS: PLEASE
ANSWSER ASAP: ALL 3 AND WILL RATE U ASAP.
The logistic growth model describes population growth when
resources are constrained. It
is an extension to the exponential growth model that includes an
additional term introducing
the carrying capacity of the habitat.
The differential equation for this model is:
dP/dt=kP(t)(1-P(t)/M)
Where P(t) is the population (or population density) at time t,
k > 0 is a growth constant,
and M is the carrying capacity of the habitat. This...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
Question Details The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 in by 10% in 10 years, what will be the population in 50 years? (Round your answer to the nearest person.) persons How fast is the population growing at t-50? (Round your answer to two decimal places.) persons/yr + Ask Yc Question Details
9. The population of a small town in Montana in 1985 was found to be given by P = 30,000e" where t is time measured from 1985. a. What was the population in the year 2000? b. When will the population of that town reach 90,000. 9. The population of a small town in Montana in 1985 was found to be given by P = 30,000.025 where t is time measured from 1985. a. What was the population in the...
Suppose that a population of hacteria grows according to the logistic differential equation dP =0.01P-0.0002P2 dt where Pis the population measured in thousands and t is time measured in days. Logistic growth differential equations are often quite difficult to solve. Instead, you will analyze its direction field to acquire infom ation about the solutions to this differential equation. a) Calculate the maximum population M that the sumounding environment can austain. (Note this is also calked the "canying capacity"). Hint: Rewrite...
(1 point) Any population, P, for which we can ignore immigration, satisfies dP Birth rate – Death rate. dt For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the form dP аP? — ЬР with a, b > 0. dt This problem investigates the solutions to...
The population of fish, P, in a lake is a function of time, t, measured in years. The rate of change of P is given by 7600e0.4t fish/year. dt(19 + e0.4t)2 dp dt a. Graph on the domain [0, 20]. Make sure your graph is properly labeled. b. Estimate the change in population on the time interval 0 s t š 20 years. Use 10 intervals, each lasting two years. Use rate of change data from the left side of...
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