## GOODMAN 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. Libniz

$y=ne^{kt}$

2. Libniz

n is beginning y is end

3. GOODMAN

Correct. Dont know where to start on this problem.

4. Libniz

so in beginning there was 400

5. Libniz

so plug in 400 for n

6. Libniz

plug in what for y?

7. GOODMAN

5000?

8. Libniz

yes

9. Libniz

$5000=400 e^{kt}$

10. Libniz

t represent time , what time do you see there

11. GOODMAN

t would go in as 1.5

12. Libniz

1 1/4= 1.25

13. GOODMAN

I knew that.

14. Libniz

let's go with that

15. GOODMAN

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

16. Libniz

yes

17. Libniz

your job is to find k

18. GOODMAN

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

19. Libniz

exactly

20. GOODMAN

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

21. Libniz

not what I would do

22. GOODMAN

How would you set it up?

23. Libniz

I would divide both sides by 400 first

24. GOODMAN

Ohh okay.

25. Libniz

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

26. Libniz

now take ln of both sides

27. GOODMAN

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

28. GOODMAN

Wouldnt ln and e cancel eachother out though?

29. Libniz

yes

30. GOODMAN

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

31. Libniz

yes

32. GOODMAN

k=2.02?

33. Libniz

yes

34. GOODMAN

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

35. GOODMAN

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

36. Libniz

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

37. GOODMAN

Ohh okay. So intead of 1.25, just t?

38. Libniz

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

39. Libniz

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

40. GOODMAN

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

41. GOODMAN

*15000

42. Libniz

exactly , this time you are finding the 't'

43. GOODMAN

I got 0.5438

44. GOODMAN

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

45. GOODMAN

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

46. Libniz

yes

47. GOODMAN

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

48. Libniz

what?

49. GOODMAN

.5438

50. Libniz

yes ,

51. Libniz

it will take .5438 hours

52. GOODMAN

okie dokes.

53. GOODMAN

Thanks youuuu!!

54. Libniz

nice to meet you

55. GOODMAN

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