Mr. Mudd gives each of his children $2000 to invest as part of a friendly family competition. The competition will last 10 years. The rules of the competition are simple. Each child can split up his or her $2000 into as many separate investments as they please. The children are encouraged to do their research on types of investments. The initial investments made may not be changed at any point during the 10 years; no money may be added and no money may be moved. Whichever child has made the most money after 10 years will be awarded an additional $10,000. The table shows the investment made by each of Mr. Mudd's children, and what happened to their investment over the decade long friendly competition. Child Performance of investments over the course of the competition Albert $1000 earned 1.2% annual interest compounded monthly $500 lost 2% over the course of the 10 years $500 grew compounded continuously at rate of 0.8% annually Marie $1500 earned 1.4% annual interest compounded quarterly $500 gained 4% over the course of 10 years Hans $2000 grew compounded continuously at rate of 0.9% annually Max $1000 decreased in value exponentially at a rate of 0.5% annually $1000 earned 1.8% annual interest compounded biannually (twice a year) (Score for Question 1: _of 7 points) 1. What is the balance of Albert's $2000 after 10 years?Answer: (Score for Question 2: _ of 5 points) 2. What is the balance of Marie's $2000 after 10 years? Answer: (Score for Question 3: _ of 2 points) 3. What is the balance of Hans' $2000 after 10 years? Answer: (Score for Question 4: _ of 5 points) 4. What is the balance of Max's $2000 after 10 years? Answer: (Score for Question 5: _of 1 points) 5. Who is $10,000 richer at the end of the competition? Answer:1. Arjun incorrectly writes log, x + log, y-log, zas a single logarithm. log, x + log, y-log, z = log, (x+ y-z) Where did Arjun make errors? Explain his errors and the properties of logarithms that leads to the correct answer. State the correct answer. Answer: (Score for Question 2: _ of 7 points) 4 In 2-1 2. Helen and Stephen both simplify the exponential expression e wit # In 2-1 In 23 1/8 Helen: 3 #In 2-1 Stephen: e = =e3 = eve2 Unfortunately, they both made an error. Identify where each person made his or her error and explain in words what he or she did wrong. Then, correctly simplify the expression. Answer:3. Answer the questions. a. Solve the logarithmic equations. 1. log, 64 = m 2. log, n = 3 3. log 4096 =3 4. 10g32 9 = 3 b. Study the pattern in the equations. Use your observations to solve the equation for a. Express your answer in terms of x. log,, 2" =3