Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Unit Conversion with Exponential Decay The exponential function
a. What is the weekly decay factor? Find a formula that gives the amount
b. What is the yearly decay factor? Find a formula that gives the amount
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Round each percentage increase or decrease that you calculate to the nearest tenth of a percent. Percentage Decay Rate from Decay FactorAn exponential function has a decay factor of 0.06. What is the percentage decay rate?arrow_forwardHalf-Life of Radioactive Iodine A student is trying to determine the half-life of radioactive iodine-131. He measures the amount of iodine-131 in a sample solution every 8 hours. His data are shown in the table below. a Make a scatter plot of the data. b Use a calculator to find an exponential model. c Use your model to find the half-life of iodine-131. Time h Amount of 131I(g) 0 8 16 24 32 40 48 4.80 4.66 4.51 4.39 4.29 4.14 4.04arrow_forwardChanging UnitsA certain quantity has a yearly decay factor of 0.99.What is its century decay factor?arrow_forward
- U.S. Population The U.S. Constitution requires a census every 10 years. The census data for 17902010 are given in the table. a Make a scatter plot of the data. b Use a calculator to find an exponential model for the data. c Use your model to predict the population at the 2020 census. d Use your model to estimate the population in 1965. Year Population in millions Year Population in millions Year Population in millions 1790 1800 1810 1820 1830 1840 1850 1860 3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 1870 1880 1890 1900 1910 1920 1930 1940 38.6 50.2 63.0 76.2 92.2 106.0 123.2 132.2 1950 1960 1970 1980 1990 2000 2010 151.3 179.3 203.3 226.5 248.7 281.4 308.7arrow_forwardRound each percentage increase or decrease that you calculate to the nearest tenth of a percent. Function from Initial Value and Percentage Decay RateSuppose that f is an exponential function with a percentage decay rate of 5 and that f(0)=6. Find a formula for f(x).arrow_forwardThe Decibel scale Exercise S-7 through S-10 refer to the decibel scale. If one sound has a relative intensity one-tenth that of another, how do their decibel levels compare?arrow_forward
- Ice CubeAn ice cube that is 3 cm on each side is melting at a rate of 2 cm3per min. How fast is the length of the side decreasing?arrow_forwardRound each percentage increase or decrease that you calculate to the nearest tenth of a percent. Percentage Growth Rate from Growth FactorAn exponential function has a growth factor of 1.06. What is the percentage growth rate?arrow_forward
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