. . . .SHow ALL WORK including computations even if calculator used. Worksheet is 15 points ..... Question 1 ('7 points) On Jan 1, 2010, Catvitte and Kitten Town each had 20 cats. One year later, Catville and Kitten Town both had 80 cats. Suppose the annual growth of cats in Catville is linear (i.e., has a constant of change) and in Kitten Town it increases by the same ratio each year (i.e., has a constant ratio of change). Let x be the number of years since Jan 1, 2010. (a). (4 points) The population of cats in Catville is a function, C, of x. The population of cats in Kitten Town is a function, K, of x. Complete the tables below. Tip: Write below the table what you do to each function each time you increase x by 1. You can leave your answers as computations. For example, if the answer is 2 - 2 - 3 write that or 22 - 5 instead of 20. (b). (1 point) When 3: increases by 1, how does C (x) change? What about K (x)? Answer in complete sentences and be specific. (c). (2 points) Are the rates of change of cats with respect to years constant in Kitten Town and/ or Catville? How do you know? Justify for both and determine some of the con- stant/ average rates of change. Background: Chances are you have or will find yourself searching for a loan. It could be for school, a car, a house, the list goes on. Whatever the reason, understanding loans is important for making economically informed decisions. Most types of loans are calculated via EXPONENTIAL FUNCTIONS so now is a perfect time to talk about loans! Have you heard of APY or APR? APY stands for Annual Percentage Yield. It takes into account if the interest rate is compounded (i.e., collected yearly / monthly / etc). The APY is the 1-year interest rate. APR stands for Annual Percentage Rate. It does not show the affects of compounding, however an APR does compound so it is helpful to convert APRs to APYs to compare them. 1) Note: The terms one-year scale factor is the same thing as the oneyear ratio (or portion) flf'ET) Question 2 (8 points) Suppose tomorrow you are taking out a loan for a used car and are choos ing between Ao Credit (calculates interest yearly) and jour Credit (calculates interest daily). You don't expect to pay any of your loan for 3: years. The money you owe, in thousands of dollars, on your car loan 1' years after tomorrow is A(x) = 16(125)' at Ao Credit or _ 0.235 365-? (a). (1 point) What do A(0) and 1(0) equal and represent? Write in a sentence and be specic. at Jour Credit. Explore on Desmoscorn /calcu1ator/ nctc2wye4j. (b). (1 point) For Ao Credit, fill in the blanks. (One-year percent change is equivalent to APY.) The one-year: scale factor is and percent change is (c). (2 points) For Iour Credit, fill in the blanks. Calculate the scale factor up to 4 decimals. To determine the one-year scale factor, rewrite ] (x) as I (x) = 16(b-V) for an appropriate constant b. (Term: the Jour Credit loan is a 23.5% APR compounded daily.) The one-year: scale factor is and percent change is (d). (2 points) In complete sentences, justify which loan you prefer. Be specic and convincing. (e). (2 points) Suppose A(t) = 32. Verbally explain what i means in this context and approxi- mate t up to 2 decimals by graphing (eg on Desmos). Write in a complete sentence