Task 1: Comparing financial situations [ 18 marks ] 1. You may have to decide to invest your money using simple interest, compound interest, or an annuity. Determine the final amount after 20 years with a 5% annual interest rate if you invest $10,000 in: a. An account that earns simple interest. [3 marks] b. An account that earns compound interest (compounded annually). [3 marks] c. An annuity where you invest the $10,000 spread over the course of 20 years annually (note: determine the regular annual payment first). You can use a TVM solver instead of the formula if you wish.[3 marks] d. Which option you would choose and why? Make sure to include if each situation is reasonable and other factors that may affect your decision. [2 marks] 2. Determine the final amount after 20 years with a 5% annual interest rate if; a. You invest $10,000 in an account that earns compound interest (compounded quarterly). [3 marks] b. You invest in an annuity where you invest $500 every 3 months over the course of 20 years compounded quarterly. You may use a TVM solver if you wish. [3 marks] c. Discuss which option you would choose and why. Make sure to include if each situation is reasonable and other factors that may affect your decision. [1 mark] Task 2: Comparing powers [ 6 marks ] 4 Write two simplifying powers question that has the answer Eyis for each situation below. Simplify the question and show all steps for full marks. a. The 1st question must begin with two radicals. [2 marks] b. The 2nd question must use at least three of the following rules: [4 marks] - powers of powers - multiplying powers with like bases - dividing powers with like bases - hegative exponents - powers of a quotient. Task 3: Exponential Decay [16 marks] 1. Write an equation to model each situation, with clearly defined variables: o The value of my car was $25,000 when | purchased it. The car depreciates at rate of 25% each year. [3 marks] o Light intensity in a pond is reduced by 12% per metre of depth, relative to the light intensity at the surface [3 marks] 2. The population of a small mining town was 13, 700 in 2000. Each year, the population decreases by an average of 5%. o Explain why the situation described is an example of exponential decay [2 marks] o Write an exponential function that models this situation. Explain each part of the equation. [4 marks] o Use your equation (trial and error) to estimate what year the population will drop below 5000 people. [4 marks]