SOLUTION: hey I am having some issues trying to layout this word problem and could use some help please. A population of 1000 bacteria is growing exponentially and doubles in number ever

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: hey I am having some issues trying to layout this word problem and could use some help please. A population of 1000 bacteria is growing exponentially and doubles in number ever      Log On


   

Question 1027424: hey I am having some issues trying to layout this word problem and could use some help please.
A population of 1000 bacteria is growing exponentially and doubles in number every 17 mins. How long until there are 3600 bacteria?
it then asks to show hand work using algebra and either a common log or natural log. I am confused on what to do.
Thanks for all your help.
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
p, the initial population
y, the amount of bacteria
x, the amount of time, in minutes

You might consider a continuous exponential growth model; and use k, a constant.
highlight_green%28y=pe%5E%28kx%29%29

Find a formula for k.
ln%28y%29=ln%28pe%5E%28kx%29%29
ln%28y%29=ln%28p%29%2Bln%28e%5E%28kx%29%29
ln%28p%29%2Bkx%2Aln%28e%29=ln%28y%29
kx%2A1=ln%28y%29-ln%28p%29-------* you may use this one again later.
highlight_green%28k=%281%2Fx%29ln%28y%2Fp%29%29
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The description tells you that for x=17, y%2Fp=2. Also that population will double every 17 minutes.
k=%281%2F17%29ln%282%2F1%29
k=0.04077
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Your more specific model is highlight%28y=1000%2Ae%5E%280.04077x%29%29.
You do the rest. *