A species of bacteria has a population of 250 at 6 a.m. It doubles every 8 hours. Determine the function that models the growth of the population. Determine the population at 9 p.m.?

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Answer 1 · 2018-05-28T10:50:41

6 a.m. to 2 p.m. population reaches 500.

Your equation is

(it is exponential function)

#P = P_0timese^(kt)#

#P_=# is the initial population

t is time which is 15 hours.

First, You can compute k (growth rate)

#500=250timese^(ktimes8)#

#2 = e^(ktimes8)#

#ln2 = ktimes8#

#k= 0.0866# #(hour)^-1#

Now you can calculate the final population

#P=250timese^(0.0866times15)#

#P=917#

which is greater than 500.