Chapter 1 - Problem Solving and Critical Thinking - Chapter 1 Test - Page 46: 16

(a) Estimation is a process to guess or figure about any project or work before starting it. These are approximated answers to questions that can arise in our mind. There are several number of estimation methods to solve different types of computations, activities, or production. The methods can be like rounding of figures, taking help of various graphs, technology, or mathematical models, etc. In the year 1968, grade A percentage in the high school was 17.6%. In the year 2010, grade A percentage in the high school was 48.4%. Average yearly increase in percentage of grades of A can be 48.4%-7.6%/2010-1968 =0.7% Thus, the increase in grade percentage from the year 1968 to the year 2010 is approximately 0.7% per year. (b) Estimation is a process to guess or figure before starting of any project or work. These are approximated answer to a question that can arise in our mind to start guessing anything. There are several number of estimation methods to solve different types of computation, activity, or production. These methods can be rounding of figures, taking help of various graphs, technology, mathematical models, etc. Observe the given bar graph again. Grade A percentage in the year 1968 was 17.6%. When calculated the average increase in percentage in part (a), this is found to be 0.7%. This shows the average pattern of increase in percentage in grade A. Generalizing this fact gives the estimated mathematical model for estimating the percentage in grade A. Therefore, this can be\[p=17.6+0.7x\] where p percentage in grade A is found after the x years. (c) Estimation is a process to guess or figure about any project or work before a start. These are approximated answers to a question that can arise in our mind before starting or guessing anything. There are several numbers of estimation methods to solve different types of computation, activity, or production. These methods can be rounding of figures, taking help of various graphs, technology, mathematical models, etc. Now mathematical model\[p=17.6+0.7x\] of part (b) can be used to project the percentage increase in grade A after x years. In this way, in the year 2020, that is, after 52 years, increase in grade A is p=17.6+0.7 =17.6+36.4 =54% Thus, the projected percentage increase in grade A after 52 years is 54%.

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