The size of an exponentially growing bacteria colony doubles in 3 hours. How lon

Question

The size of an exponentially growing bacteria colony doubles in 3 hours. How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.

Explanation / Answer

Say at time t=0 hours, the number N of bacteria is a. Clearly, N = a.2^(t/3) (Since y=2^x provides a function that causes y to double as x increases by 1, so 2^(x/3) would cause y to double as x increases by 3) Why is this multiplied by a? Look: t=0 --> N = a.2^0 = a (as I have stated in my model for your situation in the first line) Now we want the value of t when N=3a (triple the original size), so, 3a =a.2^(t/3) --> 3 = 2^(t/3) --> ln(3) = (t/3)ln 2 --> t/3 = ln(3) / ln(2) --> t = 3ln(3) / ln(2) --> t = ln(3^3)/ln(2) --> t = ln(27)/ln(2) That is your exact answer in hours, where obviously ln is the 'natural log or log to the base 'e''. I have made the working/modelling clear, and assume you know how to deal with exponents and logarithms. For your decimal form, punch that into a calculator and give the answer to 2.d.p (I'm sure you're more than capable). Have a nice day :) Note: Collin's answer is wrong. Also, how can 4 hours 30 mins = 4.30 hours?! 4 hours 30 mins clearly equals 4.5 hours... Source(s): Elementary maths

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