The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a culture doubles approximately every 30 min. (a) If the initial population is 100, determine the function Q(t) that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes

The equation that expresses the growth of the number of cells of this bacterium as a function of time t (in minutes) is Q(t) = 100e^0.023t.

Let the number of bacteria cells present be Q

Given that;

Initial population of the bacteria is 100, this is is an exponential growth problem.

Q(0) = 100

Q(30) = 200

From;

Qt =Qoe^rt

Where r is the growth constant and t is the time taken.

200 = 100e^r(30)

200/100 = e^r(30)

2 = e^r(30)

ln 2 = lne^r(30)

0.693 = 30r

r = 0.693/30

r = 0.023

So we can write a general equation;

Q(t) = 100e^0.023t

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Step-by-step explanation:

The equation for the number of cells after t minutes is given by the following formula:

In which Q(0) is the initial population and r is the growth rate.

Initial population of 100

So

Doubles after 30 minutes.

So Q(30) = 200.

We use this to find r

So

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

312312

step-by-step explanation: