Thread: What will be a function to represent the number of bacteria after t hours ?

At the start of an experiment, there are 100 bacteria in a petri dish. The bacteria grow exponentially at a rate of 0.2% per hour.

a.) How many bacteria will be present in the petri dish after 5 hours?

b.) How Long will it take for the number of bacteria to double ?

Writing the exponential growth/decay equation
A = Aoe^kt where A = amount at time t, Ao = amount at time t = 0, k = a constant.
So after one hour
1.002 Ao = Aoe^(k*1) (and Ao cancels)
ln 1.002 =k
0.002 = k
so we can write
A = Aoe^0.002t (where t is in hours)
after 5 hours
A = 100e^0.002*5
A = 100*e^0.01
A = 100*1.01
A = 101 after 5 hours
for number to double,
2Ao = Aoe^0.002T
2 = e^0.002t
ln2 = 0.002t
t = (ln2)/0.002
t = 346.57 hours for number to double.

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