2. Compact florescent light bulbs save energy when compared to traditional incandescent bulbs. Our green energy campaign includes efforts to get local residents to change their incandescent bulbs to florescent bulbs. Initially 184 households make the change. Market studies suggest that, in the absence of limiting factors, we could increase that number by 20% each month. In our target area, there are 222,824households, which we take as the limiting value. Make a logistic model that gives the number of households converting to florescent bulbs after t months. (Use t as your variable. Round r to three decimal places.) N(t) =

3. In a city of half a million, there are initially800cases of a particularly virulent strain of flu. The Centers for Disease Control and Prevention in Atlanta claims that the cumulative number of infections of this flu strain will increase by 40% per week if there are no limiting factors. Make a logistic model of the potential cumulative number of cases of flu as a function of weeks from initial outbreak, and determine how long it will be before 100,000 people are infected. (Round your answer to two decimal places.) weeks

4. The following table shows natural gas production N in trillions of cubic feet in the United States t years after 1940.

t = years since 1940	N = cubic ft. in trillions
0	3.75
10	8.48
20	15.09
30	23.79
40	21.87
50	21.52
60	24.15

(a) Make a logistic model for N as a function of t.

(b) Graph the data and the logistic model

(c)Which year's production was farthest from the prediction of the logistic model? (d) What does the logistic model predict for the amount of natural gas that will be produced in the long run? Note: In other contexts, this would be known as the carrying capacity. (Use the model found in part (a).

5. Suppose a population is growing according to the logistic formula

N =

450

1 + 3e^0.41t

where t is measured in years.(a) Suppose that today there are 300 individuals in the population. Find a new logistic formula for the population using the same K and r values as the formula above, but with initial value 300. (Round equation parameters to two decimal places.) N = (b) How long does it take the population to grow from 300 to 380 using the formula in part (a)? (Round your answer to two decimal places.)

t

6. Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded

N =

148

1 + 3.6e^2.61t

where t is measured in years and N is measured in thousands of tons of fish.

(a) What is the r value for the Eastern Pacific yellowfin tuna? r = per yr

(b) What is the carrying capacity K for the Eastern Pacific yellowfin tuna? K = thousand tons (c) What is the optimum yield level? thousand tons