In Problem 14, suppose we have the additional information that the population of alligators on the grounds of the Kennedy Space Center in 1993 was estimated to be 4100. Use a logistic model to estimate the population of alligators in the year 2020. What is the predicted limiting population? [Hint: Use the formulas in Problem 12.
The estimated population of alligators in the year 2020 is 6572 and the predicted limiting population is 6693.
Given, that in 1980, the population of alligators on the Kennedy Space Center grounds was estimated to be 1500 and it was estimated to be 4100 in 1993 and 6000 in 2006. We have to find estimated population of alligators in the year 2020 and the predicting limiting population.
Here, we have initial population,
We will use the following formula to find the estimated population of alligators in the year 2020,
To find the values of and A, we will use the following formulas from problem 12,
We will find the values of p1 and A, using the formulas from equation (2 and 3),
One will use these values of p1 and A in equation (1) to find the estimated population of splake in the year 2020.
To find the estimated population of alligators in the year 2020, we will substitute t=40 and other values from step1 and step3,
Hence, the estimated population of alligators in the year 2020 is 6572.
Thus, the predicted limiting population is 6693.
It was noon on a cold December day in Tampa: 16°C. Detective Taylor arrived at the crime scene to find the sergeant leaning over the body. The sergeant said there were several suspects. If they knew the exact time of death, then they could narrow the list. Detective Taylor took out a thermometer and measured the temperature of the body: 34.5°C. He then left for lunch. Upon returning at 1:00 p.m., he found the body temperature to be 33.7°C. When did the murder occur? [Hint: Normal body temperature is 37°C.]
In Problem 21 it is observed that when the velocity of the sailboat reaches 5 m/sec, the boat begins to rise out of the water and “plane.” When this happens, the proportionality constant for the water resistance drops to b0 = 60 N-sec/m. Now find the equation of motion of the sailboat. What is the limiting velocity of the sailboat under this wind as it is planning?
A rotating flywheel is being turned by a motor that exerts a constant torque T (see Figure 3.10). A retarding torque due to friction is proportional to the angular velocity v. If the moment of inertia of the flywheel, is I and its initial angular velocity is , find the equation for the angular velocity v as a function of time. [Hint: Use Newton’s second law for rotational motion, that is, moment of inertia * angular acceleration = sum of the torques.]
94% of StudySmarter users get better grades.Sign up for free