## anonymous 3 years ago A bacteria culture will grow from 400 to 5000 in 1 1/4 hours. a) Find the constant k for this bacteria using growth formula, y=ne^kt, and write the growth equation. b)Use your equation to predict how much longer it will take the 5000 bacteria to become 15000 bacteria.

1. anonymous

$y=ne^{kt}$

2. anonymous

n is beginning y is end

3. anonymous

Correct. Dont know where to start on this problem.

4. anonymous

so in beginning there was 400

5. anonymous

so plug in 400 for n

6. anonymous

plug in what for y?

7. anonymous

5000?

8. anonymous

yes

9. anonymous

$5000=400 e^{kt}$

10. anonymous

t represent time , what time do you see there

11. anonymous

t would go in as 1.5

12. anonymous

1 1/4= 1.25

13. anonymous

I knew that.

14. anonymous

let's go with that

15. anonymous

k. so the equation is $5000=400e ^{k(1.25)}$

16. anonymous

yes

17. anonymous

your job is to find k

18. anonymous

Hmm...take ln of both sides and bring exponent down then solve for k?

19. anonymous

exactly

20. anonymous

$\ln(5000)=k(1.25)\ln400e$

21. anonymous

not what I would do

22. anonymous

How would you set it up?

23. anonymous

I would divide both sides by 400 first

24. anonymous

Ohh okay.

25. anonymous

$5000/400=e ^{k(1.25)}$

26. anonymous

now take ln of both sides

27. anonymous

$\ln(25/2)=k(1.25)lne$

28. anonymous

Wouldnt ln and e cancel eachother out though?

29. anonymous

yes

30. anonymous

So basically, to get k, you would divide ln(25/2) by 1.25?

31. anonymous

yes

32. anonymous

k=2.02?

33. anonymous

yes

34. anonymous

lol thanks. so to rewrite the equation, i would just plug everything in?

35. anonymous

$5000=400e ^{2.02(1.25)}$

36. anonymous

close but to be more general you use t instead of specific time

37. anonymous

Ohh okay. So intead of 1.25, just t?

38. anonymous

$y=400e ^{2.02(t)}$

39. anonymous

that way you can find y for any t value you plug in

40. anonymous

So on b, you would plug n as 5000 and y as 1500?

41. anonymous

*15000

42. anonymous

exactly , this time you are finding the 't'

43. anonymous

I got 0.5438

44. anonymous

Because you divide by 5000 on both sides. Getting: $\ln(3)=(2.02)\ln(e)$

45. anonymous

And then divide by ln(2.02) Did I do it right?

46. anonymous

yes

47. anonymous

Thank God. lol. But would that be like 5 mins?

48. anonymous

what?

49. anonymous

.5438

50. anonymous

yes ,

51. anonymous

it will take .5438 hours

52. anonymous

okie dokes.

53. anonymous

Thanks youuuu!!

54. anonymous

nice to meet you

55. anonymous

Nice to meet you too. It was good working with you.