2log3 () - log3 (x +2) = 0 d. log2 (z) - log2(2 +2) = 3 -1082(2 - 1) 5. Algebraically find the coordinates of the point of intersection of f() = ( ) and g(x) = (27+3 ) accurate to 2 decimal places. Illustrate graphically using an appropriate scale. 6. In January of 2011, the population of a coastal Canadian city was 610 000. It was predicted that the population of the city would increase at the rate of 2.6% per year over the next 30 years. a. Determine an equation to represent the population of the city, P, as a function of the number of years t since January 2011. b. In what year will the population hit 1 million? c. Determine how many years it will take for the population to double, to the nearest year. d. Write the equation in part a) as an exponential function with base 2. 7. A sample of 320 mg of lodine-131 is stored in a laboratory for 40 days. At the end of this period only 10 mg remain. a. What is the half-life of the lodine-131? b. How long would it take for 90% of the lodine-131 sample to decay? 8. A $1000 investment earns interest at a rate of 4.2% per annum, compounded monthly. Another investment of $1600 earns interest at a rate of 3.6% per annum, compounded semi-annually. How long, if ever, will it take for the lower initial investment to be worth more than the higher one ? 9. Sandra noticed that a rapid growing algae was beginning to spread on the pond behind her house. The first time she noticed it, she estimated that it covered an area of 50 cm. When she went back 15 hours later to check, she estimated that it covered an area of 75 cm a. What area of the pond's surface would the bacteria cover if she went to check on the pond 2 days after her initial encounter? b. If the pond is somewhat circular in shape with a diameter of 450 metres, estimate how many days it would take the algae to cover 75% of the pond's surface? 10. Solve for x to three decimal places of accuracy. a. 2(56z ) - 9(547 ) + 10(527) - 3=0 b. log3 (x) + log, (z) = 5