A culture starts with 8600 bacteria. After one hour the count is 10,000.

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.) 

 bacteria 

(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.) 
 hr
Oct 21st, 2017

Denote the number of bacteria by n(t). Then n(t) = n_0 e^(kt) is an exponential function.

n(0) = 8600 = n_0, so n(t) = 8600 e^(kt).

Since n(1) = 8600 e^k = 10000, e^k = 10000/8600 = 1.163, k = ln(1.163) = 0.151, and n(t) = 8600 e^(0.151t).

(b) n(2) = 8600 e^(0.151*2) = 11600

(c) n(t) = 8600 e^(0.151t) = 2*8600 when e^(0.151t) = 2; 0.151t = ln(2)

t = ln(2)/ 0.151 = 4.6 hours

Apr 17th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Oct 21st, 2017
...
Oct 21st, 2017
Oct 21st, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer