# Math

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I'm not sure how to do this question

7. The growth of bacteria in culture can be described by the equation
N1 = N0e'
where N is the number of bactena at any time t, No is the initial number of bacteria, and k
is a constant. The time taken for growth to double the number of bacteria of a particular
strain (the 'doubling time') was 30 mm. A culture was started with 200 bacteria of this
strain
Determine the followmg (giving appropnate units in each case)
(a) the value of k for this strain (2]
(b) the rate of increase m bacterial number when the number in the colony
was 2000 131
(c) the minimum number of bacteria in this culture (1]

for a i calculated k =0.023 or (ln 2)/30
for c i think it would be at t = 0
Nt = No.e^(k0)
Nt = No.e^0
Nt = No.1
Nt = No = 200

i don't know how to do b and im not sure if im right with a and c please help

• Math -

N1 = N0e'
is wrong, and you quote a doubling time im millimeters.
To obtain help, you need to be more careful posting your questions.

• Math -

First of all your opening equation should have been
N1 = N0 e^(kt), where t is in minutes.

Does 30 mm mean "30 minutes" ? (I assumed that)

I did get the same value of k.
N = 200 e^(.023105t)

the rate of increase is the derivative of your function, so
dN/dt = 200(.023105) e^(.023105t)

So we now have to find the value of t when N = 2000131

2000131 = 200 e^(.023105t)
for that I got t = 398.6 minutes
(you better check my arithmetic here)

Now sub that t value back into our derivative to find the rate of change at that time.

c) is a strange question. Since it is exponential growth, the minimum value would be at the start, namely 200

• Math -

sorry it was a copy and paste job should checked it thanks for the help

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