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21. 22. Determine the value of n to the nearest tenth. Explain your strategy. a} 10" = 125 b) 3" = c) 5" = 0.01 ti) 250(1.03)" = 400 e) 1000(0.35]" = 300 E Choose 2 equations from question 21. Verify your answers numerically. Gillian takes a 300mg tablet of pain medication. The amount, A milligrams. of medication remaining in her body after t hours is given by the formula A = 300(03)'. a} Write an exponential equation that can be used to determine when 1 mg of medication remains in Gillian's body. b] Solve the equation in part a. 24. An archaeologist estimates the age of an artifact by measuring the amount of Carbon- 14 it contains. The artifact originally contained 200 pg of Carbon-l4. Now it contains 25 pg of Carbon-l4. The half-life of Carbon-l4 is about 5730 years. What is the age of the artifact to the nearest hundred years? 25. The resale value of a used vehicle is given by the formula V = C(l r)", where V dollars is the resale value, C dollars is the original price, 1' is the rate of depreciation as a decimal, and n is the age of the vehicle. a] A certain vehicle depreciates at a rate of 20% per year. The original price of the vehicle was $36 000 and its resale value after it years is $7549.74. Write an exponential equation that can be used to determine the age of the vehicle. b) Solve the equation in part a. c) How do you know your answer in part b is correct? 14. The formula m = 3.5(05) gives the mass, m milligrams, of radioactive Iodine in a sample t days after the initial measurement. Determine the mass of radioactive Iodine after each number of days. a) 2 days b) 4 days c) 16 days 'I 5. Solve for x. Assume x is positive. Show your work. a) x2 = 100 b) x' = 64 .1. 1 c) x2 = 9 d) x3 = 8 18. The formulaA = P(l + 1')" gives the amount,A dollars, of a compound interest investment. In the formula, P dollars is the principal invested, i is the annual interest rate expressed as a decimal, and n is the number of years. Shelley invests $500 with interest compounded annually. The amount of the investment after 6 years is $651. Determine the annual interest rate. 3 17. The formula B = (imamE gives the bird inhalation rate, B cubic metres of air per day, for a bird with mass M kilograms. a) Rewrite the formula using radicals. 1:} Calculate the inhalation rate for each bird. i) a 4.5-kg bald eagle ii] a 8.0-kg Canada goose r.) Determine the mass of a bird whose inhalation rate is twice that of the bald eagle. d} Is the mass in part c twice that of the bald eagle? Explain. 18. Rewrite each set of numbers as powers of the same base. a} 4, 16, 32 b) %, 25, 125 c) 9, 31, 243 Solve algebraically. a142" = 45 b) 5'E = 625 c) 32*\" = 9 d)10"\"= 10\"\" e) 43x2 = 32;\" n 25'\"l = 125*? Choose 2 equations from question 19. a} Explain ho'wr you solved the equations. b]: Use graphing technology to verify your answers to the equations in part a
