Question

M 6. The equation for logistic growth has the general form y = 1+ Be-M -M , where M, B, and k are positive constants and M represents the maximum level that y can obtain. Suppose that a lake is stocked with 100 fish. After 3 months there are 250 fish. A study of the ecology of the lake predicts that the lake can support 1000 fish. Find a logistic function for the number NO) of fish in the lake months after it has been stocked. Find B knowing the initial population is 100 fish. Using B, find k, then write the function below. May use your calculator, but all work must be shown. N(O) = ? 7. Using your graphing calculator, sketch the graph of the function in question 6 on the grid below. 1000 900 800 600 500 400 3001 100 12 20 8. Forensic scientists use the following law to determine the time of death of accident or murder victims. If T denotes the temperature of a body + hours after death, then T = T. +(T-T.)(0.97)', where T, is the air temperature and T) is the body temperature at the time of death. John Doe was found murdered at 9:00pm on Saturday, November 1 in his house when the room temperature was 72°F and his body temperature was 84°F. Find the time, day and date he was killed. Assume John's normal body temperature at the time of the murder was 98.6°F. (May use your calculator, but all work! must be shown)

Answer 1

- € Equation for logistic growth is 1+ Be-Mkt Herre M=1000 N (O) = 100 M(3): 250 Thea Nit) - Ma - 10 1+ R (takt -1000K use N (0) - 100 100 000 1+B loot 100 B = 1000 100 B = goo a B=9] use. N(3) = 250 250 Ooo 1+92 3000K 3oook 250 + 2250 e - 30Dok e = 0.333 - 3000 keln (0.333) = Scanned with CamScanner

ke -ln 13) - long (3) 3000 30 OO Mence 1000 Nit) -1000tin (3) 17 9 7 7300 coal. NIE) 3 - It g. 13 Scanned with CamScanner

1000 Plotting: y=— -X 1+9. 33. 2000 -50 50