# Cultivation of Bacteria culture

Document Type:Math Solving

Subject Area:Mathematics

### Document 1

For instance, transgenic reaps have a potential of decreasing weed killers thus allow farmers to spray the weeds without affecting the crops. Asexual reproduction in plants and bacteria allows scientists to obtain genetically matching populations (Ravikumar, S. , et al). For instance, in the year 1996, the Dolly lamb was born from chromosomal substance that was taken from an adult sheep to generate an animal with same chromosomal DNA with donor animal. Bacterial organisms are amongst plentiful life forms on the planet. Also, the bacteria help in digestion and break down of particles of food taken in by human beings which allows humans to process their food. Derivatives A derivative is a way of showing or representing rate of change that is the amount a function is changing at a given point.

Stationary point is defined with respect to differentiation function and it is a point whereby a given specific function at which the derivative is equal to zero. It is a point where a function increases or decreases (Jian, Z. H. A is the constant and t represent the amount of time in which the bacteria is placed in the culture. The maxima of a function F(x) refers to all the points in the respective graph resulting to local maximums. In this case, the maxima of a function f(x) is a local maximum point, say x=a which when it moves to the left then the respective values of the function tend to decrease. On the contrary, the minima of the function f(x) are the points of x which upon moving either towards the right or left will increase the value of f(x).

To affirm the values of the maxima or minima then the gradient of the function must be equal at all these points. The growth system of the bacteria is exponential in nature and hence the resultant differential equations must be exponential. For example, if the number of bacteria in a certain culture increases to 800 from a previous value of 500 in 3hours and the equation follows the exponential model, then the expected exponential equation with k and t as constant and time respectively will be; The function f(t)= Aekt. This is the exponential function/expression for the bacteria culture in question. Ultimately, the first and second derivatives for this differential equation will be substantial in highlighting the maximum, minimum and the other stationary points for the function.

Therefore, f(t)= Aekt, Where A= f (0). In this case, A = 500 and f(t) = 8000 Therefore, the equation is 8000= 500 e 3k Where k is a constant and t=3hrs Hence, the number of bacteria in say 4 hours will be, Here we start by looking at the value of k, a constant and in this case, it will be expressed as K= 0. 9242 The value of k is gotten by making it the subject of the formula. After doing this, then the respective values of the known variables are substituted. Ultimately, after getting the values of k, then we will use it to get the value or the number of bacteria at a unit time which is the main core of our thesis. The value of k will make the equation complete and hence it will be possible to estimate the population of the bacteria at different time intervals.

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