SOLUTION: An infectious strain of bacteria increases in number at a relative growth rate of 200% per hour. When a certain critical number of bacteria are present in the bloodstream, a person

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Question 297219: An infectious strain of bacteria increases in number at a relative growth rate of 200% per hour. When a certain critical number of bacteria are present in the bloodstream, a person becomes ill. If a single bacterium infects a person, the critical level is reached in 43 hours. How long will it take for the critical level to be reached if the same person is infected with 16 bacteria? (give answer to two decimals in hours).
Am I on the right track... 16*10^(2.0*43)= 1.6*10^87 ? If I am... how to convert to hours?
Thank you much for your help.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Check your equation.
At time t=0 hr, N=N0=16.
At time t=1 hr, N=16%2B2%2816%29=48.
What function are you using to model? Since the growth rate is proportional to the amount of current value, the mathematical model to use would be the exponential function.
An exponential function would be look like,
N=N0%2Ae%5E%28kT%29
You could then use N%281%29 to find k.
Since you already know N0, you could plug in T=43 to find the critical value.
Hopefully that steers you in the right direction.
Re-post if you need more help.