Math 30-2 Exponent Questions

Name: ID: A Numeric Response 1. (1 point) A research lab has a 12 mg sample of a radioactive substance. The amount of the substance, A(t), left in the sample can be modelled by the halflife function A(t):12[%]3 Where trepresents the time, in days, after the initial time. How long does it take for the sample to reduce to one quarter its initial amount? (Record your answer in the numerical response box from left to right.) 2. (1 point) How many times more intense is an 8.5 earthquake than an 8.0 earthquake? Round your answer to the nearest hundredth. (Record your answer in the numerical response box om left to right.) 3. (1 point) Solve the following exponential equation. x_ 1_ Sex 6 "[216] (Record your answer in the numerical response box from left to right.) Name: ID: A 4. (1 point) Thorium-227 has a half-life of 18.4 days. The remaining amount of a SO-mg sample of thorium227 can be modelled by the equation 1 A(t)=50[%]m where A(t) is the amount of thorium-227 remaining, in milligrams, and t is the time in days. Determine the amount of thorium-227 remaining after 10 days, to the nearest milligram. (Record your answer in the numerical response box from left to right.) Problem 1. (1 point) In terms of hydrogen ion concentration, how much more acidic is a solution with a pH of 4.0 than a solution with a pH of 5.5? Round your answer to the nearest tenth. Show your work. Recall that pH, p(x), is dened by the equation 1706) = ~10g x where the concentration of hydrogen ions, x, in a solution is measured in moles per litre. 2. (1 point) The sound level of a concert is 102 dB. Determine the sound level, to the nearest decibel, of the concert if the intensity increases by 0.04 W/mz. Show your work. Recall that sound level, ,6, in decibels, is dened by the equation =10(log 1+ 12) where 1 is the sound intensity in watts per square metre. Name: ID: A 3. (1 point) The growth of a plant during a eightmonth period is modelled by the exponential function f(X) = 3(1.25)x where x) represents the height, in centimetres, at the end of each month and x represents the time in months. Determine when the plant will reach a height of 12 cm, to the nearest tenth of a month. Show your work. 4. (1 point) _ Which expression has the greater value? Show all of your work. A: logz 16+log28 B:log[1]%log[;]32 2 2 5. (1 point) Consider the equation: 8'H = l6"+3 a) Solve this equation algebraically using logarithms. b) Solve this equation using a different algebraic strategy. 6) Which strategy do you prefer? Explain why