Name Modeling 2 - ICE-Growth Rates, Scale, and Inflation The following table shows inflation rates for several decades into 2020 dollars. 2000-2020 53% 2010-2020 19% 1990-2020 102% 1980-2020 232% Time span Inflation The following table shows the nominal (unadjusted) prices for gold over several years, Complete the table showing gold prices in constant 2020 dollars. (Round to the nearest cent.) Show your work below the table. [(5 x 0.2)(table) + (4 x 1)(work) = 5 pt) 2020 2010 2000 1990 1980 Year $1636.35 $1179.25 $273.68 $516.92 $381.73 Nominal (unadjusted) price per ounce Constant (adjusted) price per ounce in 2020 dollars - la. 1980 $516.92 1b. 1990 $381.73 1c. 2000 $273.68 1d. 2010 $1179.25 1d. 2020 It is not necessary to adjust the 2020 price, but you must still fill in the table above in constant 2020 dollars! $1636.35 129 Name Modeling 5 - ICE - Exponential Modeling, Logarithms 1. In 1970, an industrial waste site contained an estimated 350 tons of contaminated soil. Special cleaning crews were contracted to clean up the site. The crews can remove 20% of the contaminated soil each year. (1 pt) How do we know this describes an exponential function? a. b. Write a formula that calculates A, the amount of waste remaining (in tons), t years after 1970. (1 pt) C. What amount of waste remained in 1979? Round to the nearest whole number. Use correct units. (1 pt) d. When is the amount of waste expected to reach 1 ton or less? Express your answer as a year (like 1974) and not in years since 1970 (like t = 4). (1 pt) e. In 2020, which is 50 years after they started cleaning up the site. Is it reasonable to think that plugging t = 50 into the formula will give an accurate measurement of the waste that remains at the site? Why or why not? (1 pt) 171 Name Modeling 2 - ICE-Growth Rates, Scale, and Inflation The following table shows inflation rates for several decades into 2020 dollars. 2000-2020 53% 2010-2020 19% 1990-2020 102% 1980-2020 232% Time span Inflation The following table shows the nominal (unadjusted) prices for gold over several years, Complete the table showing gold prices in constant 2020 dollars. (Round to the nearest cent.) Show your work below the table. [(5 x 0.2)(table) + (4 x 1)(work) = 5 pt) 2020 2010 2000 1990 1980 Year $1636.35 $1179.25 $273.68 $516.92 $381.73 Nominal (unadjusted) price per ounce Constant (adjusted) price per ounce in 2020 dollars - la. 1980 $516.92 1b. 1990 $381.73 1c. 2000 $273.68 1d. 2010 $1179.25 1d. 2020 It is not necessary to adjust the 2020 price, but you must still fill in the table above in constant 2020 dollars! $1636.35 129 Name Modeling 5 - ICE - Exponential Modeling, Logarithms 1. In 1970, an industrial waste site contained an estimated 350 tons of contaminated soil. Special cleaning crews were contracted to clean up the site. The crews can remove 20% of the contaminated soil each year. (1 pt) How do we know this describes an exponential function? a. b. Write a formula that calculates A, the amount of waste remaining (in tons), t years after 1970. (1 pt) C. What amount of waste remained in 1979? Round to the nearest whole number. Use correct units. (1 pt) d. When is the amount of waste expected to reach 1 ton or less? Express your answer as a year (like 1974) and not in years since 1970 (like t = 4). (1 pt) e. In 2020, which is 50 years after they started cleaning up the site. Is it reasonable to think that plugging t = 50 into the formula will give an accurate measurement of the waste that remains at the site? Why or why not? (1 pt) 171