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Marianna [84]
2 years ago
11

If 3,000 bacteria, with a growth constant (k) of 2.8 per hour, are present at the beginning of an experiment, in how many hours

will there be 15,000 bacteria?
Mathematics
1 answer:
Ivenika [448]2 years ago
4 0

Given:

Initial number of bacteria = 3000

With a growth constant (k) of 2.8 per hour.

To find:

The number of hours it will take to be 15,000 bacteria.

Solution:

Let P(t) be the number of bacteria after t number of hours.

The exponential growth model (continuously) is:

P(t)=P_0e^{kt}

Where, P_0 is the initial value, k is the growth constant and t is the number of years.

Putting P(t)=15000,P_0=3000, k=2.8 in the above formula, we get

15000=3000e^{2.8t}

\dfrac{15000}{3000}=e^{2.8t}

5=e^{2.8t}

Taking ln on both sides, we get

\ln 5=\ln e^{2.8t}

1.609438=2.8t                  [\because \ln e^x=x]

\dfrac{1.609438}{2.8}=t

0.574799=t

t\approx 0.575

Therefore, the number of bacteria will be 15,000 after 0.575 hours.

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