Math 30-2 Name: Part C: Written Response: (10 marks) 1. The Place for Stuff is having a sale. The price of all stock will be reduced by 15% at the start of each week until all the stock is sold. The exponential function that models the price of a sofa from the start of the sale is C(t) = 2000(0.85) where C(t) represents the co the cost of the sofa at the end of the week and t represents the time in weeks since the sale began. (3 marks) a. After which week did the sofa cost less than half of the initial price? Explain. b. Dimitri bought the sofa for $1288.25. In which week did Dimitri buy the sofa? Explain. 2. The population of British Columbia is given from 2007 to 2011. (5 marks) Year 2007 2008 2009 2010 2011 Population (millions) 4.3096 4.384 4.4599 4.5297 4.5733 a. Construct a scatter plot to display the data (use years since 2007 as the x, and population in millions as the y). Give an appropriate window setting. b. Use exponential regression to define a function that models the data. C. Assuming the same growth rate as in part b., estimate the population of British Columbia in 2020. Describe your process. d. Assuming the same growth rate as in part b., when would you expect the population to reach 4 700 000? Describe your process. cosiq fentloeb eno erb 3. The element Polonium-210 decays naturally over time. An equation relating time and the percentage of Polonium-210 remaining is given by t=-96.336logP where t represents the time in years and P represents the percentage of Polonium- 210, as a decimal, that remains. A sample of Polonium-210 is taken from a reactor. Estimate the time at which 40% of it will remain. Explain what you did. (2 marks)