Question 4: 27 Marks Suppose the functions f, g and h are dened by f(x) = 3"'+3'\"""3 and g(x) = 1034 (X + 2)+log4 (3) log.; (5} log4 (2x 3) and h(x) = 6\""+159'Jr respectively. (4.1) Write down the sets Dr, 09 and 0;, that represent the domains of f, g and h respectively. (3) (4.2) Solve the equation f (X) = 12 for X. (8) (4.3) Solve the inequality g(X) = 0 for X. (8) (4.4) Solve h(x) = 8 for X. Leave the answer in terms of In, where necessary. (8) Question 5: l4 Marks A culture starts with 230 bacteria. After 30 minutes the number of bacteria is 1 150. (5.1) Find a formula for the number of bacteria after ihours. (5) (5.2) Use the formula to nd the number of bacteria after 1 hour. (4) (5.3) After how many minutes will the number of bacteria be 125 times the original number? Leave (5) the answer in terms of In but in simplied form. Question 6: 14 Marks The half-life of radium226 is 1590 years. (6-1) (4) A sample of radium226 has a mass of 100 mg. Find a formula for the mass of the sample that remains after 1' years. (6.2) Find the mass after 1000 years. (4) (6.3) When will the mass be reduced to 30 mg? (6) Question 7: 10 Marks The population of a small village grows exponentially. At time t the number N( t) of people in the village is given by the formula NU) = Noe\" where No represents the initial size of the population and r is the relative rate of growth. Suppose the population increases from 800 to 1200 over a period of 3 years. (7.1) Find the value of r (in terms of In) and then write down the equation of the function N that (5) models the number of people in this population after 1' years (7.2) Use the equation in (7.1) to calculate the estimated size of the population after 12 years