SOLUTION: A culture atarted with 6000 bacteria. After 4 hours, it grew to 7800 bacteria. Predict how many bacteria will be present after 18 hours. Round your answear to the nearest whole num

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Question 332866: A culture atarted with 6000 bacteria. After 4 hours, it grew to 7800 bacteria. Predict how many bacteria will be present after 18 hours. Round your answear to the nearest whole number.
I have to use the expoential formula which is N=NoE-kt
I dont really understand how to get the inc. or the answear if you could help it would be much appriciated
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A culture atarted with 6000 bacteria. After 4 hours, it grew to 7800 bacteria. Predict how many bacteria will be present after 18 hours. Round your answear to the nearest whole number.
I have to use the expoential formula which is N=NoE-kt
.
Given:
+N=NoE%5E%28-kt%29+
where
N is amount after time t
No is the initial amount
k is the constant rate of growth/decline
t is time
.
Plugging in what is given by the problem we have:
+7800+=+6000E%5E%28-k4%29+
Solve for k:
+7800%2F6000+=+E%5E%28-k4%29+
+13%2F10+=+E%5E%28-k4%29+
+ln%2813%2F10%29+=+-k4+
+ln%2813%2F10%29%2F4+=+-k+
+-ln%2813%2F10%29%2F4+=+k+
+-0.0656+=+k+
.
Our general equation is now:
+N=+6000E%5E%280.0656t%29+
Plugging in 18:
+N=+6000E%5E%280.0656%2A18%29+
+N=+6000%283.256%29+
+N=+19539+