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ollegr [7]
3 years ago
15

A population of bacteria is growing according to the exponential model P = 100e.70t, where P is the number of colonies and t is

measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]
A) 0.7
B) 1.6
C) 5.7
D) 7.2
Mathematics
2 answers:
Reika [66]3 years ago
6 0
T=(log(300÷100)÷log(e))÷0.7
T=1.6
OleMash [197]3 years ago
5 0

Answer:

The correct option is B). 1.6 years

Step-by-step explanation:

The model for the population of bacteria is growing by :

P = 100\cdot e^{0.70t}

where P is the number of colonies and t is measured in hours.

Now, we need to find after how many hours will 300 colonies be present

So, Putting value of P = 300 in the above model and obtain the value of t

\implies 300=100\cdot e^{0.70t}\\\\\implies 3=e^{0.7t}\\\\\text{taking natural log ln on both the sides}\\\\\implies \ln 3=\ln e^{0.7t}\\\\\implies \ln 3=0.7t\\\\\implies t=\frac{\ln 3}{0.7}\\\\\implies t=1.6\:\: years

Therefore, The correct option is B). 1.6 years

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