Question 1(Multiple Choice Worth 1 points) (07.07 MC) Given g is a solution to the differential equation / (t. y), with initial condition g(0) = 1, find lim g(). jim 9(1) - Question Question 1 (Not Answer\fQuestion 2(Multiple Choice Worth 1 points) (07.07 MC) Without solving the logistic differential equation, find a model for the population of manatees in a section of the Indian River Lagoon that has a carrying capacity of 50; if the population started with five manatees, and after two years, increased to 12 manatees. O p(1) = 50 1+9e-3.5r O p(t) =- 50 1-98 0.527 O p(!) = 50 1+90 527 O p(t) = 50 1498 0.527 Question 3(Muluple Choice Worth 1 points) (07.07 MC) A virus spreads through a population according to the logistic differential equation . = 0.04y(1-y). where y is the proportion of the population (0 s y's 1) that has the virus at time . What proportion of the population has the virus when it is spreading the fastest? 25 OQuestion 3(Multiple Choice Worth 1 points) (07.07 MC) A virus spreads through a population according to the logistic differential equation = 0.04y(1-y). where y is the proportion of the population (0 s y s 1) that has the virus at time t. What proportion of the population has the virus when it is spreading the fastest? O 1 25 O 01 Question 4(Multiple Choice Worth 1 points) (07.07 MC) A local conservation group releases 50 Pine Barrens tree frogs into a neighboring forest with a carrying capacity of 500 tree frogs. Assume there are no other tree frogs in the forest, and this species of tree frogs follows a logistic growth model. After 2 years, there are 80 tree frogs in the forest. How long will it take (in t years) for there to be 160 tree frogs? 5.356 years 4.009 years M EQuestion 4(Multiple Choice Worth 1 points) (07.07 MC) A local conservation group releases 50 Pine Barrens tree frogs into a neighboring forest with a carrying capacity of 500 tree frogs. Assume there are no other tree frogs in the forest, and this species of tree frogs follows a logistic growth model. After 2 years, there are 80 tree frogs in the forest. How long will it take (in t years) for there to be 160 tree frogs? O 5.356 years 4.009 years 10.425 years O 267.804 years Question 5(Multiple Choice Worth 1 points) (07.07 MC) The differential equation _ = k(M -y)y shown has a particular solution with the initial condition f(2) = 2 dx MQuestion 5(Multiple Choice Worth 1 points) (07.07 MC) The differential equation 24 - k(M -y)y shown has a particular solution with the initial condition /(2) = 2. Let y = h(x) be a particular solution to the given differential equation f(x, y) with h(4) = 10. Find lim (5-h(x) -f(x) -6 6-MX) f(x) - 6-h(x) im F(x) - 6 M C C hp6-h(x) Let y = h(x) be a particular solution to the given differential equation f(x, y) with h(4) = 10. Find lim f(x) -6 O lim 6-1(x) 7 (x ) - 6 lim 6-h(x) 7 ( x ) - 6 (6 1x) -6 7(x) - 6 m S h(x ) M hp