An economist tracks the price of a certain item at the beginning of several years and compiles the following table. Year 2013 2014 2015 2016 Price in dollars 265.50 273,47 281.67 290.12 (a) Show that the price is growing as an exponential function. (Let P be the price in dollars and t the time in years since 2013.) Calculate the ratios of new price/old price. (Round your answers to two decimal places.) P1 Ро P2 P1 Рз %3D P2 Does the table show exponential data? Yes o No (b) Find an exponential model for the data. (Round the values to two decimal places. Let t be the time in years since 2013.) P = 304.21 x 0.83 P = 260.00 x 1.12 P = 290.12 x 0.97° P = 265.50 x 1.03t P = 93.12 x 1.35t (c) At the beginning of some year, the price will surpass $344. Use the model found in part (b) to determine which year.

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Data were collected from libraries about the number of patrons who have overdue books and how long they have been using the library. Years Using Library 1 1 1.5 3 3.5 5 7 10 Number of Overdue Books 12 9 10 6 5 4 2 2 The equation ŷ = 12(0.81)x is a model that fits the data. Which of the following uses the model correctly and is an example of extrapolation?    A patron who has been using the library for 2 years is predicted to have between 7 and 8 overdue books.  A patron who has been using the library for 13 years is predicted to have between 6 and 7 overdue books.  A patron who has been using the library for 2 years is predicted to have more than 94 overdue books.  A patron who has been using the library for 13 years is predicted to have less than 1 overdue book.

An economist tracks the price of a certain item at the beginning of several years and compiles the following table. 2014 2015 273.47 281.67 2016 290.12 2013 Year Price in dollars 265.50 (a) Show that the price is growing as an exponential function. (Let P be the price in dollars and t the time in years since 2013.) Calculate the ratios of new price/old price. (Round your answers to two decimal places.) P₁. Po P2, P1 P2 Does the table show exponential data? Yes No (b) Find an exponential model for the data. (Round the values to two decimal places. Let t be the time in years since 2013.) CP= 304.21 x 0.83t P = 290.12 x 0.97t CP= 260.00 x 1.12t P = 93.12 x 1.35* P = 265.50 x 1.03t (c) At the beginning of some year, the price will surpass $344. Use the model found in part (b) to determine which year.

Violent crime rates in the United States are shown in the table for various years. Year Number of Violent Crimes per 100,00 people 1990 730 1995 685 2000 507 2005 469 2009 432 2016 386 (a) Find a linear model for f(a).  Round all numbers to 3 decimal places.

Reporting the value of assets for tax purposes. If a 3100 dollar refrigerator depreciates completely in 7 years, find a formula for its value as a function of time, x, in years. (The value you report depreciates with time, assume straight-line depreciation where the value is a linear function of time)

The simple interest on an investment is directly proportional to the amount of the investment. By investing $5800 in a municipal bond, you obtained an interest payment of $221.25 after 1 year. Find a mathematical model that gives the interest I for this municipal bond after 1 year in terms of the amount invested P. (Round your answer to three decimal places.) I= 26.215P I=221.25P I= 0.038P I= 1,283,250P I=5800P

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An economist tracks the price of a certain item at the beginning of several years and compiles the following table. Year 2013 2014 2015 2016 Price in dollars 265.50 273.47 281.67 290.12 (a) Show that the price is growing as an exponential function. (Let P be the price in dollars and t the time in years since 2013.) Calculate the ratios of new price/old price. (Round your answers to two decimal places.) P1 =   P0 P2 =   P1 P3 =   P2 Does the table show exponential data? YesNo     (b) Find an exponential model for the data. (Round the values to two decimal places. Let t be the time in years since 2013.) P = 290.12 × 0.97t P = 304.21 × 0.83t      P = 265.50 × 1.03t P = 260.00 × 1.12t P = 93.12 × 1.35t (c) At the beginning of some year, the price will surpass $325. Use the model found in part (b) to determine which year.