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The purpose of this mathematical paper is to discuss the applications of ordinary mathematical problems concerning rates of change that result in becoming variables in a problem.

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Introduction

Introduction The purpose of this mathematical paper is to discuss the applications of ordinary mathematical problems concerning rates of change that result in becoming variables in a problem. This paper will also analyze the practical uses of calculating rates, as well as focus on rates in terms of differential calculus. Background Information To be quite honest, the field of mathematics had never been my forte; I have never seemed to be able to grasp concepts that come so easily to others. However, the area of science fascinates me. Last year, in Biology class, we were appointed to complete an assignment in which we recorded the rates of enzyme reactions when different variables acted upon the substrate. I found the entire experiment intriguing, and didn't realize, until recently, that it was in any way related to Calculus. A rate of change of an object is the speed at which a variable can change over a specific period of time. ...read more.

Middle

Mathematical Applications In order to find the rate of change of an object, one would, essentially, be required to find the slope of a graph. Differential Calculus can be applied in this situation, in that by finding the derivative. For example, consider a man who is 6 feet tall and walking toward a lamppost 20 feet high at a rate of 5 feet per second. The light at the top of the lamppost (20 feet above the ground) is casting a shadow of the man. At what rate is the tip of his shadow moving and at what rate is the length of his shadow changing when he is 10 feet from the base of the lamppost? If z were to equal the distance from the tip of the shadow to the base of the lamppost, y equaled the length of the shadow, and x equaled the distance from the man to the base of the lamppost, we would also know that dx dt = -5 ft/sec From that, we could ...read more.

Conclusion

time was measured. Nine beakers with different concentrations of enzymes were utilized. Small paper discs were soaked in each of the different enzyme solutions of different concentrations, after which they were placed on the bottom of a hydrogen peroxide solution (the substrate) and timed in order to see how long it would take for the enzyme to react with the substrate and cause the paper disc to float to the top of the hydrogen peroxide solution. Concentration of Substrate Time (sec.) 0 0 0.10 10.63 0.20 5.44 0.30 4.9 0.50 4.3 0.80 2.19 1 % 1.69 2 % 1.47 3 % .97 Conclusion Differential calculus has many practical uses outside of the classroom in the 'real' world, and is a valuable tool in determining the rates of changes that are occurring, whether they be chemical reactions, such as in the case of the enzyme and substrate concentration experiment, or in other cases, such as rates of changes in the acceleration or deceleration of a car, or in the rate a rock falls off of a cliff. 2 ...read more.

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