Suppose the number of bacteria in a certain population increases according to a continuous exponential growth model. a sample of 2200 bacteria selected from the population reached the size 2300 bacteria in one and a half hours. Find the hourly growth rate parameter.

The hourly growth rate is 2%

An exponential growth is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b > 1

Let y represent the number of bacteria after x hours.

There was initially 2200 bacteria, hence a = 2200. The equation becomes:

Therefore the hourly growth rate is 1.02 - 1 = 0.02 = 2%

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The hourly growth rate parameter of the bacteria is 3%.

Step-by-step explanation:

Continuous exponential growth formula:

A= Population of bacteria after t hours

P = Initial population

r= growth rate

t= time in hours

Given that,

A sample of 2200 bacteria selected from the population reached the size 2300 bacteria in one and half hours.

A=2300, P=2200, t hours = hours,r=?

Taking ln both sides

The hourly growth rate parameter of the bacteria is 3%.

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363