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# lecture29 - Lecture 29 1 Lecture 29(Sec 5.6 Exponential...

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Lecture 29 1 Lecture 29: (Sec. 5.6) Exponential Functions as Mathematical Mod- els Exponential Growth Recall the graphs of the function y = b x , b > 1 and y = e x : Now consider the function Q ( t ) = Q 0 e kt , where Q 0 and k are positive constants:

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Lecture 29 2 Def. Let Q ( t ) > 0 be a quantity whose rate of growth at any time t is directly proportional to the amount of the quantity present at time t . Then and we model this growth by the equation The quantity is said to exhibit and k is
Lecture 29 3 ex. Suppose \$1500 is invested in an account in which interest is compounded continuously at 6% annual interest. Find a formula for the rate of change of the amount at any time t .

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Lecture 29 4 ex. A colony of viruses is growing exponentially (that is, the rate of growth is proportional to the number of viruses at any time t ). There were 500 viruses at 10AM and 20,000 at 3PM. a) Find a model for this growth.
5 b) How many will be in the colony at 6PM (approx- imately)? c) How many will there be at 8PM (exactly)?

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## This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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lecture29 - Lecture 29 1 Lecture 29(Sec 5.6 Exponential...

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