SOLUTION: After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria. I'm very conf

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria. I'm very conf      Log On


   

Question 155617: After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria.
I'm very confused by this word problem. I'd like the correct answer and to be able to learn how to come to that answer. Thank you for all your help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
OK, first, you know that you have exponential growth,
your equation looks like this,
N%28t%29=N%5B0%5De%5E%28%28alpha%2At%29%29
Use your conditions to find N%5B0%5D and alpha
.
.
.
Initially, at t=0 hours, N=100
N%280%29=N%5B0%5De%5E%28%28alpha%2A0%29%29=100
N%5B0%5D=100 since e%5E0=1
.
.
.
At 5 hours, N=500,
N%285%29=100e%5E%28%28alpha%2A5%29%29=500
e%5E%28%28alpha%2A5%29%29=5
alpha%2A5=ln%285%29
alpha=ln%285%29%2F5
alpha=0.322
.
.
.
Put it all together,
N%28t%29=100e%5E%28%280.322%2At%29%29