The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s range from 35 to 40 million per year and death rates range from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 100 billion. Use the logistic model to predict the world population in the 2,450 year. Calculate your answer in billions to one decimal place. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate.)

  24.1 billion

Step-by-step explanation:

One way to write the logistic function is ...

  P(t) = AB/(A +(B-A)e^(-kt))

where A is initial value (P(0)), and B is the carrying capacity (P(∞)). We are told to use relative population growth in the 1990s as the value for k.

In billions, we have ...

  A = 5.3

  B = 100

  k = 0.02/5.3 ≈ 0.003774 . . . . . relative growth rate at 20 M per year

  t = 2450 -1990 = 460

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

6. 104

7. 52/37

8. 2704

9. 140608

10. -52

11. |52|=52

12. 1/52

13. 156

14. 26

15. 40

16. 37

17. -364

18. 53 1/3

19. 50.96

20. 43 2/3

21. 78

22. 50.75

23. 47.63

24. 163.28

25. 10400

26. 338

27. 208

28. 2704 square inches

29. 312 square meters

30. don't know what its asking, tell me so i can tell you

31. 8490.56

32. 52 degrees would be an acute angle

33. 128 degrees

34. 20.8

35. 39

36. 208