The fish and game department in a certain state is planning to issue hunting permits to control the deer population (one deer per permit). It is known that if the deer population falls below a certain level m, the deer will become extinct. It is also known that if the deer population rises above the carrying capacity M, the population will decrease back to M through disease and malnutrition. a. Discuss the reasonableness of the following model for the growth rate of the deer population as a function of time: dP =rP(M-P) (P-m) dt where P is the population of the deer and r is a positive constant of proportionality. Include a phase line. b. Explain how this model differs from the logistic model dP =rP (M-P) dt Is it better or worse than the logistic model? c. What happens if P > M for all t? d. What happens if P < M for all t? e. Discuss the solutions to the differential equation. What are the equilibrium points of the model? Explain the dependence of the steady- state value of P on the initial values of P. About how many permits should be issued?

Given that a zone has 275 household with car and 275 household without car and the average trip generation rates for each group is respectively 5.0 and 2.5 trips per day. Assuming that in the future, all household will have a car, find the growth factor and future trips from that zone, assuming that the population and income remains constant.

Determine whether the following scenarios are linear or exponential. As summer approaches, I noticed that for every increase in 5 degrees, the number of people I see at the pool increases by about 3. The amount of Francium,a radioactive element, decays by about 3.1% every minute. The number of flu cases increases by about 1.6% per month during flu season. Based on Mrs. Olivet's Test 4 results, students tended to score about 4 more points on their test for every hour they studied. The percentage of the population that has been vaccinated for COVID-19 increased by about 0.25 percentage points every day in January. The population of bugs in Monica's walls decreased by 80% every week while the exterminator was treating her home. During a rainstorm the reading from the rain gauge increased by a quarter inch every hour. Selene didn't want her parents to notice she was stealing candy from the jar, so every day she only ate 1/8 of what was left. While writing an essay, Carson writes 7…

This exercise uses the population growth model. It is observed that a certain bacteria culture has a relative growth rate of 11% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 24. Find the projected population after 24 hours for the following conditions. (Round your answers to the nearest whole number.) (a) No antibiotic is present, so the relative growth rate is 11%.bacteria (b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.bacteria