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1 1. Population Growth. The 2000 census found a U.S. population of about 281 million, with an estimated growth rate of 0.7% per year. Write an equation for the U.S. population that assumes exponential growth rate at this rate. Use the equation to predict the U.S. population in 2100. Q = U.S. population Q0 = initial value is the 2000 population = 281 million r = 0.7% per year = 0.007 per year Q = Q0 x (1 + r)t = 281 million x (1 + 0.007) t = 281 million x (1.007) t Use the equation to predict the U.S. population in 2100: = 281 million x (1.007) 100 = 564 million 2. a. Create an exponential function of the form Q = Q0 x (1 + r)t to model the situation described. Be sure to identify both variables in your function. b. Create a table showing the values of the quantity Q for the first 10 units of time c. Make a graph of the exponential function The population of a town with an initial population of 60,000 grows at a rate of 2.5% per year. Q = population of _______________________ Q0 = initial value of the population is _____________ r = 2.5% per year = _____________ Q = Q0 x (1 + r)t Q = 60,000 x (1 + Year 0 1 2 3 4 5 6 7 8 9 10 )t Population Chapter 9C Practice Problems 2 Chapter 9C Practice Problems 3 3. Declining Population. China’s one-child policy was originally implemented with the goal of reducing China’s population to 700 million by 2050. China’s population was about 1.2 billion. Suppose China’s population declines at a rate of 0.5% per year. Write an equation for the exponential decay of the population. Will this rate of decline be sufficient to meet the original goal? Q = China’s population Q0 = initial value of the population is r = -0.5% per year = Q = Q0 x (1 + r)t 4. a. Create an exponential function of the form Q = Q0 x (1 + r)t to model the situation described. Be sure to identify both variables in your function. b. Create a table showing the values of the quantity Q for the first 10 units of time c. Make a graph of the exponential function A town with a population of 10,000 is losing residents at a rate of 0.3% per month because of a poor economy. Q = population of _______________________ Q0 = initial value of the population is _____________ r = _____% per year = _____________ Q = Q0 x (1 + r)t Q = _______ x (1 + Month 0 1 2 3 4 5 6 7 8 9 10 )t Population Chapter 9C Practice Problems 4 Chapter 9C Practice Problems