Find the equation for the population (P) in terms of time (t) in minutes.

Algebra
Tutor: None Selected Time limit: 1 Day

Javier is working in a lab testing bacteria populations. After starting out with a population of 295 bacteria, he observes the change in population and notices that the population doubles every 23 minutes.

Step 1: Find the equation for the population in terms of time in minutes. Round values to 3 decimal places.

Apr 14th, 2015

The equation can be written as N(t) = N(0) * 2^(kt) where N(t) is the number of bacteria at the time t, and k is a constant. Note that N(0) = 295. Since the population doubles every 23 minutes, 23k = 1 or k = 1/23.

Finally, N(t) = 295*2^(t/23) = 295*2^(0.043t). 

Apr 14th, 2015

okay i'm really confused because I was taught to do it using P(t) = P little 0 a^t can you show me that way


Apr 15th, 2015

If you write the equation as P(t) = P0at,   then P0 = 295 and P(23)/P0 = 2 = a^23. 

Take the logarithm of both sides: 23a = ln 2; a = ln(2) /23 = 0.030 and the equation will be 

P(t) = 295*0.030^t .

Apr 15th, 2015

Correction. The last two lines should look as

Take the logarithm of both sides: 23 ln a = ln 2; ln(a) = ln(2) /23 = 0.030; a = e^(0.030) = 1.030

 and the equation will be  P(t) = 295*1.030^t .


Apr 15th, 2015

thank you I understand now.

Apr 15th, 2015

You are welcome.

Apr 15th, 2015

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