2. [2/3 Points] DETAILS PREVIOUS ANSWERS MY NOTES In this question, you will be asked to represent a word problem in mathematical terms. You will only have to enter your final answer into WebAssign, but you should keep hold of the paper that shows your intermediate calculations. Suppose that you borrow 40000 dollars from a bank, and that the bank charges 5 percent annual interest, compounded monthly, on the loan. You make monthly payments of 150 dollars at the end of each month. Write down a word equation that can be used to calculate the amount that is owed on the loan at the end of the month in terms of the amount owed at the start of the month. Writing the monthly balance (i.e. how much is owed) as y , translate your word equation into mathematical terms. Simplify this equation. If we write Yn+1 = ayn+b, what are the values of a and b? a = -1.05 X b = -150 What is the value of yo? Yo = 40000 Submit Answer 3. [2/3 Points] DETAILS PREVIOUS ANSWERS MY NOTES In this question, you will be asked to represent a word problem in mathematical terms. You will only have to enter your final answer into WebAssign, but you should keep hold of the paper that shows your intermediate calculations. Suppose that you deposit 4000 dollars in a savings account, on which the bank pays 5 percent interest, compounded monthly. Just before the end of each month, you make an additional deposit of 100 dollars. Write down a word equation that can be used to calculate the balance of the account at the end of the month in terms of the balance at the start of the month. Writing the balance as yn , translate your word equation into mathematical terms. Simplify this equation. If we write Yn+1 = ayn + b, what are the values of a and b? a = 0 x b = 100 What is the value of yo? yo = 4000-/4 Points] DETAILS MY NOTES If you were to plot the terms of the difference equation yn+1 = 0.6y, + 3, starting with the initial value yo = 9, which word or words from the following list would correctly describe your graph? For this question, if the graph is constant then JUST select 'constant'. O constant increasing O decreasing monotonic O oscillatory unbounded O asymptotic to the line If you were to plot the terms of the difference equation yn+1 = -9yn - 2. starting with the initial value yo = -2, which of the following word or words would correctly describe your graph? For this question, if the graph is constant then JUST select 'constant'. O constant increasing decreasing monotonic O oscillatory O unbounded O asymptotic to the line Submit Answer -/4 Points] DETAILS MY NOTES Wanda wants to take out a loan. She can afford to make monthly payments of 300 dollars and wants to pay the loan off after exactly 25 years. What is the maximum amount that Wanda can afford to borrow if the bank charges interest at an annual rate of 10 percent, compounded monthly? (Give your answer, in dollars, correct to the nearest dollar.) Need a hint on how to approach this question? amount she can borrow: Submit Answer -/4 Points] DETAILS MY NOTES John borrows 30000 dollars from a bank that charges interest at an annual rate of 10 percent, compounded monthly. Calculate the monthly payment that John would have to make in order for the loan to be paid off after exactly 30 years. (Give your answer, in dollars, to the nearest cent. You should not include the dollar sign or any commas in your answer.) monthly payment: Submit Answer -/4 Points] DETAILS MY NOTES James wants to take out a loan. Suppose he can afford to make monthly payments of 200 dollars and the bank charges interest at an annual rate of 8 percent, compounded monthly. What is the maximum amount that James could afford to borrow if the loan is to be paid off eventually? (Give your answer, in dollars, correct to the nearest dollar.) amount he can borrow: Submit Answer-/4 Points] DETAILS MY NOTES Carolyn wants to retire in 20 years time, and so decides to start a new retirement savings account. She wants to accumulate 1000000 dollars by the time she retires. Initially, Carolyn deposits 2000 dollars into the account. She will make further deposits at the end of each month. The account will earn interest at annual rate 10 percent, compounded monthly. How much will she have to deposit into the account each month in order to reach this target after 20 years? (Give your answer, in dollars, correct to the nearest cent.) monthly deposit: Submit Answer -/5 Points] DETAILS MY NOTES Gary has just retired, and has 500000 dollars in his retirement account. The account will earn interest at an annual rate of 8 percent, compounded monthly. At the end of each month, Gary will withdraw a fixed amount to cover his living expenses. Gary wants his savings to last exactly 30 years. How much money can he withdraw each month? (Give your answer in dollars, correct to the nearest cent.) monthly withdrawal: What is the maximum amount that Gary can withdraw each month if he wants his savings to last indefinitely? monthly withdrawal: Submit Answer1. [-/6 Points] DETAILS MY NOTES For each of the following, find the derivative, f'(x). (a) f (x) = 4x +5 f' ( x ) = [ (b) f (x) = -5x +4 f' ( x ) = (c) f (x) = 12 f' ( x ) = [ (a f (a) = x f' ( x ) = (e) f (2) = f' ( x ) = (F) f (2) = Vx2 f' ( x ) = [ symbolic formatting help Submit Answer 2. [-/2 Points] DETAILS MY NOTES You are given the function below. f (x) = Vx2 Find the following values. Give your answers correct to at least four decimal places. (a) f(10) = (b) f ' ( 10 ) = Submit Answer 3. [-/4 Points] DETAILS MY NOTES If we have the curve y = VT, find the y value and the slope of the curve when x = 16. y = slope = Hence, find the equation of the tangent line to the curve at x = 16, writing your answer in the form y = mx + c. What are the values of m and c? m = C= Submit Answer 4. [-/4 Points] DETAILS MY NOTES If we have the curve x, find the y value and the slope of the curve when x = 2. y = slope = Hence, find the equation of the tangent line to the curve at x = 2, writing your answer in the form y = mx + c. What are the values of m and c? m = C= Submit Answer 5. [-/2 Points] DETAILS MY NOTES Find the equation of line that is tangent to the curve y = " at x = 2. (You do not need to enter this into WebAssign.) Using this tangent line, find the approximate value of 1.995. Enter your answer to at least four decimal places. tangent line approximation of 1.993 = Calculate the exact value of 1.995 using your calculator. Enter your answer to at least four decimal places. Calculated value of 1.993 =[ Submit Answer-/6 Points] DETAILS MY NOT The function y = f (x) has the following graph: 8 a b C d e f x Points a though g have x-values 1, 1.5, 2, 2.5, 3, 3.5 and 4, respectively. At which points does the limit of the function exist? Oa O c O d Oe Of O g At which points is the function continuous? O a O b O c O d Oe Of O g At which points is the function differentiable? O a O b O c O d Oe Of O g Submit