Gregory Furda
Math 110
5/21/14
Technical Writing Assignment #2 In 1985, two friends, Dempsey and Tucker, started saving their money. The total amount of money in Dempsey's account is represented by the equation Ad(t)=7.53(1.041)t. The total amount of money in Tuckers account is represented by the equation At(t)= 10.42+ 0.53t. The purpose of this assignment is to use mathematical equations and calculations, as well as tables and graphs to compare the total amounts of money in each account and determine when the savings accounts will be equal and when one account will become larger than the other. The first step is to write out the equations as well as any other known data. The equation that represents Dempsey's account is Ad(t)=7.53(1.041)t. The equation that will represent Tucker's account will be At(t)=10.42+0.53t. The units of measurement for the money has been changed to "thousands of dollars" so the 7.53 will represent the original $7530 Dempsey had in his account and the 10.42 will represent the $10,420 that Tucker origninally had in his account. This will need to be changed to interpret the results correctly at the end. This account value will be called (A) and will be the dependent variable. The independent variable will be the time in years since 1985 and will be called (t). The growth factor for Dempseys account can be found within the parenthesis of the equation. This equation is exponential and represents an increasing rate of change. A growth factor of 1.041 represents an increase of 4.1% per year. To change a growth factor to a percent, subtract 1 from the growth factor, then move the decimal to the right 2 places. The slope of the equation for Tucker's account is .53 and represents an increase of $530 per year. Again, move the decimal to the right 2 places, and since this equation is linear the slope represents a constant rate of change. To create a table that will be used to sketch a graph, simply input the different values for (t) into the seperate equations to determine the correct value for (A). For example, for At, insert 5 for (t), which would look like, a(t)=10.42+.53(5). The result is 13.05, and insert this numbers into the table. So the point would be (5,13.07). Do this for all values to create the table. After all the points for the table are determined they can be transfered to a graph and sketched. It is clear, by looking at the graph, that between year 32 and year 33 the account balances are equal and after year 33 Dempseys account balance will become greater than Tucker's.