1. 2002 BC Question 5NO CalculatorWarm Up Consider the differential equation (a)The slope field for the given differential equation is provided. Sketch the solution curve that passes through the point (0,1) and sketch the solution curve that passes through the point (0, -1). b) Let f be the function that satisfies the given differential equation with the initial condition f(0)= 1. Use Euler’s Method, starting at x = 0 with a step size of 0.1, to approximate f(0.2). Show the work that leads to your answer. c) Find the value of b for which y = 2x + b is a solution to the given differential equation. Justify your answer. d) Let g be the function that satisfies the given differential equation with the initial condition g(0) = 0. Does the graph of g have a local extremum at the point (0,0)? If so, is the point a local maximum or local minimum? Justify your answer.

3. Mrs. Chumas has a juicy rumor that she is dying to spread… but there are rules… Once you know you can only tell one other person between each class. How many periods will it take before everyone knows the rumor?

4. 12345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 Person who was told the rumor

5. L is the carrying capacity Logistics Curve equation:

6. Write a logistics model for the rumor data collected in class. When was the rumor spreading the fastest? Maximum rate occurs when P = ½ L

7. The differential equation of a logistic curve looks like… Write a differential equation for the rumor data collected in class. or

8. The growth rate of a population of bears in a newly established wildlife preserve is modeled by dP/dt = 0.008P(100 – P), where t is measured in years. What was the carrying capacity for bears in this wildlife preserve? What is the bear population when the population is growing fastest? What is the rate of change of the population when it is growing the fastest?

9. The growth rate of a population of bears in a newly established wildlife preserve is modeled by dP/dt = 0.008P(100 – P), where t is measured in years. Solve the differential equation. If the preserve started with 2 bears, find the logistic model for population of bears in the preserve.

10. The growth rate of a population of bears in a newly established wildlife preserve is modeled by dP/dt = 0.008P(100 – P), where t is measured in years. With a calculator, generate the slope field and show that your solution conforms to the slope field.

11. A 2000-gallon tank can support no more than 150 guppies. Six guppies are introduced into the tank. Assume that the rate of growth of the population is dP/dt = 0.0015P (150 – P ), where t is time in weeks. Find a formula for the guppy population in terms of t. How long will it take for the guppy population to be 125?