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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 Po Does the table show exponential data? O 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.) OP = 93.12 × 1.35t OP = 265.50 x 1.03 Op = 260.00 x 1.12 Op = 290.12 x 0.97t Op = 304.21 x 0.83 (c) At the beginning of some year, the price will surpass $333. Use the model found in part (b) to determine which year.

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 Po Does the table show exponential data? O 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.) OP = 93.12 × 1.35t OP = 265.50 x 1.03 Op = 260.00 x 1.12 Op = 290.12 x 0.97t Op = 304.21 x 0.83 (c) At the beginning of some year, the price will surpass $333. Use the model found in part (b) to determine which year.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 40E
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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 Po Does the table show exponential data? O 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.) Op = 93.12 x 1.35 OP = 265.50 x 1.03 O P = 260.00 x 1.12 OP = 290.12 x 0.97t OP = 304.21 x 0.83 (c) At the beginning of some year, the price will surpass $333. Use the model found in part (b) to determine which year.
Transcribed Image Text: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 Po Does the table show exponential data? O 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.) Op = 93.12 x 1.35 OP = 265.50 x 1.03 O P = 260.00 x 1.12 OP = 290.12 x 0.97t OP = 304.21 x 0.83 (c) At the beginning of some year, the price will surpass $333. Use the model found in part (b) to determine which year.
A biologist studying the growth of an animal population has obtained the following model for the time T, in years, at which the population has reached the size N. T = 25 log(N) - 50 (a) At what time does the population reach a size of 210? (Round your answer to two decimal places.) yr (b) What was the initial population size?
Transcribed Image Text:A biologist studying the growth of an animal population has obtained the following model for the time T, in years, at which the population has reached the size N. T = 25 log(N) - 50 (a) At what time does the population reach a size of 210? (Round your answer to two decimal places.) yr (b) What was the initial population size?
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