20
assume the exponential growth model a(t)=a subscript 0 e superscript kt and a world population of 6.7 billion in 2005. if the population must stay below 21billion during the next 100 years, what is the maximum acceptable annual rate of grow

0.010423315 x 109 = 1.04 x 107 people

Step-by-step explanation:

(19 x 109) = (6.7 x 109) (e100k)

and solve for k

(19 x 109) / (6.7 x 109)  =  e100k

2.835820896 = e100k

ln 2.835820896 = ln e100k

ln 2.835820896 = 100k

k = (ln 2.835820896) / 100

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

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