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baherus [9]
3 years ago
11

Suppose that the number of bacteria in a certain population increases according to an exponential growth model. A sample of 2600

bacteria selected from this population reached the size of 2873 bacteria in two and a half hours. Find the continuous growth rate per hour. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
Mathematics
1 answer:
melisa1 [442]3 years ago
3 0

Answer: There is 3.994% continuous growth rate per hour.

Step-by-step explanation:

Since we have given that

Initial bacteria = 2600

After two and a half hours,

Number of bacteria = 2873

We need to find the continuous growth rate per hour.

As we know the equation for continuous growth rate per hour.

y=y_0e^{rt}\\\\2873=2600e^{2.5r}\\\\\dfrac{2873}{2600}=e^{2.5r}\\\\1.105=e^{2.5r}\\\\\text{Taking log on both the sides}\\\\\ln 1.105=2.5r\\\\0.0998=2.5r\\\\r=\dfac{0.0998}{2.5}\\\\r=0.0399\times 100\\\\r=3.994\%

Hence, there is 3.994% continuous growth rate per hour.

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