SOLUTION: The number of bacteria in a culture is given by the formula {{{n(t) = 1000e^0.4t}}} where t is measured in hours. What is the initial population n0 of the culture (at t = 0)? {

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Question 913470: The number of bacteria in a culture is given by the formula n%28t%29+=+1000e%5E0.4t where t is measured in hours.
What is the initial population n0 of the culture (at t = 0)? n%280%29+=+1000
Approximately how many bacteria, N, will the culture contain after 4 hours? N+=+5967.30
Because 1000e%5E%280.4%29%284%29 I checked my calculator twice why isn't this the right answer? what am I doing wrong.
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the equation should be n%28t%29+=+1000e%5E%280.4t%29

Plug in t = 4 and evaluate

n%28t%29+=+1000e%5E%280.4t%29

n%284%29+=+1000e%5E%280.4%2A4%29

n%284%29+=+1000e%5E%281.6%29

n%284%29+=+1000%284.9530324%29 This is approximate

n%284%29+=+4953.0324 This is approximate

So the approximate number of bacteria after 4 hours is roughly 4,953.0324

Round to the nearest whole number to get 4,953

Final Answer: 4,953 bacteria (approximate figure)

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
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Thanks,

Jim