SOLUTION: A population of bacteria is growing according to the exponential model P = 100e^.70t, where P is the number of colonies and t is measured in hours. After how many hours will 300 co

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Question 1034220: A population of bacteria is growing according to the exponential model P = 100e^.70t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P+=+100%2Ae%5E%28.7t%29+
+P+=+300+
+300+=+100%2Ae%5E%28.7t%29+
+3+=+e%5E%28.7t%29+
Take the natural log of both sides
+ln%283%29+=+.7t+
+.7t+=+1.09861+
+t+=+1.5694+
300 colonies will be present in 1.6 hrs
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check:
+300+=+100%2Ae%5E%28.7t%29+
+300+=+100%2Ae%5E%28.7%2A1.5694%29+
+300+=+100%2Ae%5E1.09861+
+300+=+100%2A3+
+300+=+300+
OK