SOLUTION: The bacteria E Coli are found in the human bladder. Suppose 1,000 bacteria are present at time t = 0. Then, t minutes later the number of bacteria present can be approximated by

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Question 290509: The bacteria E Coli are found in the human bladder. Suppose 1,000 bacteria are present at time t = 0. Then, t minutes later the number of bacteria present can be approximated by N(t) = 1000(3)t/12.
a) How many bacteria will be present after 40 minutes?
b) How long will it take before there are 100,000 bacteria present?
Can someone explain how to solve this problem?
Thank you, Cynthia

Found 2 solutions by nerdybill, richwmiller:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The bacteria E Coli are found in the human bladder. Suppose 1,000 bacteria are present at time t = 0. Then, t minutes later the number of bacteria present can be approximated by N(t) = 1000(3)t/12.
.
I think your equation is really:
N%28t%29+=+1000%283%29%5E%28t%2F12%29
This is an "exponential growth" equation.
Where
N(t) is the bacteria count
t is time (in minutes)
.
How many bacteria will be present after 40 minutes?
Simply substitute 40 for t and solve:
N%28t%29+=+1000%283%29%5E%28t%2F12%29
N%2840%29+=+1000%283%29%5E%2840%2F12%29
N%2840%29+=+1000%283%29%5E3.333
N%2840%29+=+38940.74
.
How long will it take before there are 100,000 bacteria present?
The 100,000 is N(t) so you would need to solve for t:
N%28t%29+=+1000%283%29%5E%28t%2F12%29
100000+=+1000%283%29%5E%28t%2F12%29
100+=+%283%29%5E%28t%2F12%29
log%283%2C100%29+=+t%2F12
12log%283%2C100%29+=+t
50.30+=+t (minutes)
.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a) plug in 40 for t and solve for N(40) ie N(t)
b) plug in 100,000 for N(t) and solve for t.
Is that supposed to be N(t) = (1000^3) *t/12
Your equation is unclear.
Use parentheses generously.
You don't have to beg to get a response. Your question, "Can someone explain how to solve this problem?" is unnecessary. Just make sure the math question is clear.