2. (1G ptsJ Assume $250 is invested at the end of each year for 10 years and the annual interest rate of r. The amount of money in your account after 10 years is 250[(1 + r)\" 1] r Am = Assume you set a goal to have $3500 after 10 years. Use a theorem from class to show that there is an interest rate r that allows you to reach your nancial goal. Strategy for Solving Optimization Problems I. Understand the problem. Read the problem multiple times. understand what is given and what we need to find. This may include drawing a picture when appropriate. Exl : we first had to understand what it meant for us to find the distance between 2 points. we needed the graph of y= Text and maybe the triangle 2. Define appropriate notation. (807 1x1 Define relevant variables needed Give appropriate equations, Give constraint equation and equation to be optimized Ex 1 Defined d , ( x,y ) , constraint equation y= 72x+4 optimization equation : d = 7x 2+ yz 3. Identify the function to be optimized. This includes identifying an appropriate domain. without a domain we cannot appropriately solve these problems Ex1 1 = 7* 2 + 92 420, x 2 - 2 domain 4. Represent the function to be optimized as a single variable equation. we only know how to find absolute extrema of single variable equations, Therefore, we use our constraint equation to write our optimization equation in terms of I vanable Gx 1 d= 7 x2+2x+4 5. Find the absolute extrema of our function. It is not enough to find local extrema P() Notice Phas a local max profit at x= 2 weeks $3 x butan absolute max profit at x= 12 weeks 12 soifwe want to find when we have max profit, we get *= 12 weeks . 6. Make sure you answer the question given. The question may ask for cost, area, dimensions write a sentence answering the specific question asked . Ex ] we had to provide the coordinate , (x,y )= (-1,12 )