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Honors Pre-Calculus Unit 1 Day 3Name:________________________________________________________PracticeUse the given tables to make an exponential model:Find an exponential model that passes through the points (0, 4) and (3, 10).Find an exponential model that passes through the points (1, 4) and (4, 7).Transformation Formula: _____________________________________________________________________________For Problems 4 - 6 assume the base of the function is 2.3678959467015..005..left15303506..006..-23495854364.004. FunctionInitial Amounty-InterceptGrowth or DecayGrowth or Decay FactorEnd Behaviorfx= 2-2xgx=6(14)-3x+5hx=2(75)2x-4hx=4(.25)-x-47. Think: How do negative exponents change the base?… rewrite the problem!right31017500824909236397008. The number of students infected with flu after t days at Springfield High School is modeled by the following function: a) What was the initial number of infected students t = 0?b) After 5 days, how many students will be infected?c) What is the maximum number of students that will be infected?d) According to this model, when will the number of students infected be 800?9. The population of Glenbrook in the year 1910 was 4200. Assume the population increased at the rate of 2.25% per year. a) Write an exponential model for the population of Glenbrook. Define your variables. b) Determine the population in 1930 and 1900. c) Determine when the population is double the original amount. 10. The half-life of a certain radioactive substance is 14 days. There are 10 grams present initially. a) Express the amount of substance remaining as an exponential function of time. Define your variables. b) When will there be less than 1 gram remaining? 41436631640610011. Rain is essential for crops to grow, but too much rain can diminish crop yields. The data gives rainfall and cotton yield per acre for several season in a certain county. a) Make a scatter plot of the data. What degree polynomial seems appropriate for modeling the data? b) Use a graphing calculator to find the polynomial of best fit. Graph the polynomial on the scatter plot. c) Use the model that you found to estimate the yield if there are 25 in. of rainfall. 30679161618100012. Otoliths (“earstones”) are tiny structures that are found in the heads of fish. Microscopic growth rings on the otoliths, not unlike growth rings on a tree, record the age of a fish. The table gives the lengths of rock bass caught at different ages, as determined by the otoliths. Scientists have proposed a cubic polynomial to model this data. a) Use a graphing calculator to find the cubic polynomial of best fit for the data.b) Make a scatter plot of the data and graph the polynomial from part (a). c) A fischerman catches a rock bass 20 in. long. Use the model to estimate the age of the bass.right6350013. Table 1 give the population of the world in the 20th century. a) Draw a scatter plot, and note that a linear model is not appropriate. b) Find an exponential function that models population growth. c) Use the model you found to predict world population in the year 2020. 4718050546100014. Much of the fish sold in supermarkets today is raised on commercial fish farms, not caught in the wild. A pond on one such farm is initially stocked with 1000 catfish, and the fish population is then sampled at 15-week intervals to estimate its size. The population data are given in table 7. a) Find an appropriate model for the data. b) Make a scatter plot of the data and graph the model you found in part (a) on the scatter plot. c) How does the model predict that the fish population will change with time? ................
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