7. Consider the polynomial p(x) =-x4 + x3 + 6x2. [12 marks] a) The degree of this polynomial is The leading coefficient is b) Is the function even, odd, both, or neither? c) Find and classify all roots of the polynomial. d) Use the above information to sketch a graph of y = p(x) .8. Use the law of logarithms to calculate the precise value of: [6 marks] a) log2 60- log2 15 b) - -log; 27 9. A bacteria culture initially has 10 bacteria and is observed to double every 1.5 hours. [10 marks] a) Find the exponential model equation for the number of bacteria in the culture after t hours. b) Find the number of bacteria after 3.5 hours. c) After how many hours will the bacteria count reach 10,000?MATH 102 Final Exam Fall 2018 8. [12 marks] a) Consider the polynomial f(x) =2x'-5x2 - 4x+ 3 i) The degree of this polynomial is The function is even / odd / neither. (Circle the correct answer). ii) Find and classify all roots of the polynomial. (Hint: one root of the polynomial is X = -1). b) A polynomial g(x) has negative leading coefficient, a double root at X = 2, and single roots at X = 3 and X = -2 . Use this information to sketch a graph of this polynomial.10. Consider the polynomial p(x) = x -7x -6. You are given that (x + 1) is a factor. [10 marks] a) The degree of the function is The leading coefficient is The function is even or odd or neither (circle the correct answer). b) Find and classify all roots of the polynomial. c) Use the information in a) and b) to sketch the graph of y = p(x) .MATH 102 Final Exam Fall 2017 11. A culture starts with 8600 bacteria. After 1 hour, the count is 10,000. [10 marks] a) Find and state the function that models the number of bacteria 21(3) aer I hours. b) Find the number of bacteria after 2 hours. c) Aer how many hours will the bacteria double