Question #74e81

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Answer 1 · 2017-12-14T17:30:17

3252 bacteria

At the start, #t=0#, the initial number of bacteria (#N_0#) is 2000. After 6 hours (#t=6#), the number of bacteria (#N#) is now 2400.

Therefore, at #t=6#, the following exponential equation can be formed (with some constant #k#).

#2400 = 2000*e^(6k)#

Divide both sides by #2000#:

#1.2 = e^(6k)#

Take the logs of both sides:

#ln(1.2) = ln(e^(6k))#

Since #ln(e^x) = x#, this can be rephrased as:

#ln(1.2) = 6k#

#k = ln(1.2)/6 = 0.03038692613#

Going back to the original equation, we can find the number of bacteria at #t=16#:

#N = 2000 * e^(0.03038692613 * 16)# = 3252