The local governing council on Echo Island has decided on a tax rebate program to stimulate the economy. The program stipulates that each tax paying citizen on Echo Island receives a $2,100.00 rebate. Economists on the Island observed that, on average, each person with a taxable income spent 83% of their rebate, and each of the people/businesses who received this money also spent 83% of what they received, and this pattern continues for 10 iterations. That is, there are 10 iterations of money spent AFTER the rebate (we will label the rebate as iteration 0). In the exercises below, you will track the effect of one citizen's rebate. So, suppose Mary Lou is a resident of Echo Island who receives a $2,100.00 rebate. Complete the exercises below to study how Mary Lou's rebate impacts the Echo Island economy through the eleven iterations (from Iteration 0 to Iteration 10). (a) Consider Iteration 6 in the applet. The spending during Iteration 6 alone injected $686.57 into the economy. Considering all spending up to the end of Iteration 6 and including the original rebate, a total sum of $ went into the economy. Excluding the original rebate, the money injected into the economy through Iteration 6 from citizens alone totaled $. (b) Consider Iteration 8 in the applet. The spending during Iteration 8 alone injected $ into the economy. Considering all spending up to the end of Iteration 8 and including the original rebate, a total sum of $ went into the economy. Excluding the original rebate, the money injected into the economy through Iteration 8 from citizens alone totaled $. (c) Consider Iteration 10 in the applet. The spending during Iteration 10 alone injected $ into the economy. Considering all spending up to the end of Iteration 10 and including the original rebate, a total sum of $ went into the economy. Excluding the original rebate, the money injected into the economy through Iteration 10 from citizens alone totaled $. (d) There is a known formula that may be used to calculate the total sum of all iterations (as in part (c) above). For a real number r and a positive whole number n, the sum of the n numbers 1, r, r2, ,rn1 may be calculated by1+r+r2+r3++rn1=(1rn)/(1r) .Then, if A is any other real number, we may distribute which givesA+Ar+Ar2+Ar3++Arn1=A(1rn)/(1r) .These sums are referred to as Geometric Series (GS). The formula to compute the sum has many applications. For example, it may be used to develop the formula for the value of an annuity. Now, apply the GS formula to Echo Island and use it to compute the sum of all money injected into the economy over all iterations in the applet. To do so, we need to use the formula A+Ar+Ar2+Ar3++Arn1=A(1rn)/(1r) .where the values to input for the variables should be: A= r= n= (e) Now, substitute the values from part (d) into the formula and evaluate. This gives

2100+2100(0.83)+2100(0.83)2++2100(0.83)111=

(1(0.83)11)/(

)=