The number n of bacteria in a culture is given by the model n= 100e^kt where t is the time in hours. if n=300 when t= 5, find the time required for the population to double in size.

The time required for the population to double in size is 3.15 hours.

Given data:

The linear model to represent the number of bacteria is,

........................................................(1)

Here, k is the constant and t is the time required for the population to double in size.

Linear model is a mathematical tool to determine the rate of decay of any substance with respect to time.

Take log on both sides of the linear model as,

If N=300 when t= 5. Then the equation is evaluated as,

For double size of population,

Then solve by substituting all the values  in equation (1) as,

Thus, the time required for the population to double in size is 3.15 hours.

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It takes 3.15 hours for the population to double in size

Step-by-step explanation:

Given:

N= 100e^kt

N = 300

t  = 5

To Find:

The time required for the population to double in size

Solution:

Step 1: Finding the value of k

-------------------(1)

ln(N) = ln(100) +kt

On substituting the given values

k =  0.2197

Now eq(1) becomes

-------------------(2)

Step 2: Finding t value

N= 200

t = 3.15

5

step-by-step explanation: