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LenKa [72]
3 years ago
7

A bacteria culture is initially 10 grams at t=0 hours and grows at a rate proportional to its size. After an hour the bacteria c

ulture weighs 11 grams. At what time will the bacteria have tripled in size?
Mathematics
1 answer:
Vladimir [108]3 years ago
5 0

Answer: It will take 11.56 hours .

Step-by-step explanation:

Exponential growth in population or size formula :

P(t)=P_0e^{rt}

, where P_0 = initial size

r= rate of growth

t= time period

As per given , we have

P_0=10 grams

At t= 1 , P(t)= 11 grams

Then,

11=10e^{r(1)}\\\\ 1.1= e^r\\\\\text{Taking natural log on both sides , we get} \\\\\ln (1.1)=r\ln (e)\\\\ r=\ln (1.1)\\\\ r=0.0953101798043\approx0.095

When, the  bacteria have tripled in size , P(t) = 3 x10 = 30

Then,

30=10e^{0.095t}\\\\ 3=e^{0.095t}

\text{Taking natural log on both sides , we get}\\\\ \ln 3=0.095t\\\\ t=\dfrac{\ln3}{0.095}\\\\ t=\dfrac{1.09861228867}{0.095}\approx11.56

Hence, it will take 11.56 hours .

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