SOLUTION: the population of a colony of bateria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colo

Algebra ->  Rational-functions -> SOLUTION: the population of a colony of bateria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colo      Log On


   

Question 271545: the population of a colony of bateria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colony to grow to 1,000 B(t)=12*e^0.2t
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the population of a colony of bacteria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colony to grow to 1,000 B(t)=12*e^0.2t
:
12%2Ae%5E%280.2t%29 = 1000
e%5E%280.2t%29 = 1000%2F12
Use the nat logs
ln%28e%5E%280.2t%29%29 = ln%281000%2F12%29
.2t%2Aln%28e%29 = ln%281000%2F12%29
nat log of e is 1, so we have
.2t = 4.22848
t = 4.22848%2F.2
t = 22.1142 hrs to reach 1000
;
Check on a calc using t=22.1142
enter: 12*e^(.2*22.1142) = 999.99 ~1000