A bacteria culture doubles every 40 minutes. A. If the initial concentration is

Question

A bacteria culture doubles every 40 minutes.

A. If the initial concentration is 20 cells/ml, construct an exponential function y=Ca^x to describe its' growth over time where x represents 40 minute time intervals.

B. Construct an exponential function y=Ca^t where t represents hours.

C. What is the hourly growth factor?

D. What is the hourly growth rate?

E. Create a table of values that shows the number of cells/mll from t=0 to t=8

t  0 1 2 3 4 5 6 7 8

y

F. Approximately how long (in hours) will it take the bacteria concentration to reach 5000 cells/ml?

I need a very detailed start to finish explanation to this problem please. Thank you!

Explanation / Answer

A) y = C*a^x

x =0 ; y = C = 20 cells/ml

y = 20*a^x

now it doubles at 40 min

so at x = 1 (i.e. 40 min) ; we have y = 2C = 40

so

40 = 20*a

a= 40/20 = 2

so y = 20*2^x ........................(ans)

B) x = 40 min interval

t = 40/60 = 0.667 hrs interval

x = t/0.667 = 1.5*t

y = 20*2^(1.5t).......................(ans)

C)

t = 1

y = 20*2^1.5

Factor = 20*2^1.5 / 20 = 2^1.5 = 2.828 ............ (ans)

D)

dy/dt = 5*2^(1.5t + 2)

E)

0......... 20

1..........56.568

2..........160

3..........452.54

4..........1280

5..........3620.3

6..........10240

7..........28963

8...........81920

F) 5000 = 20*(2^1.5t)

2^1.5t = 5000/20 = 250

taking log both sides

1.5t * log 2 = log 250

1.5t = 7.965

t = 5.31 hours

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.