Exponential Regression Equations

A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a 10-minute period. Write an exponential regression equation for the data, rounding all values to the nearest thousandth.

• y = 75.123 * e^(-0.045x)

• y = 80.456 * e^(-0.032x)

• y = 78.789 * e^(-0.050x)

• y = 82.234 * e^(-0.038x)

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The table below shows the number of new stores in a coffee shop chain that opened during the years 1986 through 1994. Using x = 1 to represent the year 1986 and y to represent the number of new stores, write the exponential regression equation for these data. Round all values to the nearest thousandth.

• y = 2.5 * (1.3)^x

• y = 3.1 * (1.2)^x

• y = 4.0 * (1.1)^x

• y = 5.2 * (1.05)^x

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A population of single-celled organisms was grown in a Petri dish over a period of 16 hours. The number of organisms at a given time is recorded in the table below. Determine the exponential regression equation model for these data, rounding all values to the nearest ten-thousandth. Using this equation, predict the number of single-celled organisms, to the nearest whole number, at the end of the 18th hour.

• 1,200

• 1,500

• 1,800

• 2,100

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The data collected by a biologist showing the growth of a colony of bacteria at the end of each hour are displayed in the table below. Write an exponential regression equation to model these data. Round all values to the nearest thousandth. Assuming this trend continues, use this equation to estimate, to the nearest ten, the number of bacteria in the colony at the end of 7 hours.

• 1,230

• 1,240

• 1,250

• 1,260

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Jean invested $380 in stocks. Over the next 5 years, the value of her investment grew, as shown in the accompanying table. Write the exponential regression equation for this set of data, rounding all values to two decimal places. Using this equation, find the value of her stock, to the nearest dollar, 10 years after her initial purchase.

• $500

• $750

• $1000

• $1250

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A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the coins that land heads up are returned to the box, and then the process is repeated. The accompanying table shows the number of trials and the number of coins returned to the box after each trial. Write an exponential regression equation, rounding the calculated values to the nearest ten-thousandth. Use the equation to predict how many coins would be returned to the box after the eighth trial.

• Approximately 125 coins

• Approximately 250 coins

• Approximately 500 coins

• Approximately 750 coins

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The accompanying table shows the amount of water vapor, y, that will saturate 1 cubic meter of air at different temperatures, x. Write an exponential regression equation for this set of data, rounding all values to the nearest thousandth. Using this equation, predict the amount of water vapor that will saturate 1 cubic meter of air at a temperature of 50°C, and round your answer to the nearest tenth of a gram.

• 82.3 grams

• 83.5 grams

• 84.7 grams

• 85.9 grams

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The table below, created in 1996, shows a history of transit fares from 1955 to 1995. On the accompanying grid, construct a scatter plot where the independent variable is years. State the exponential regression equation with the coefficient and base rounded to the nearest thousandth. Using this equation, determine the prediction that should have been made for the year 1998, to the nearest cent.

• A) $1.50

• B) $1.75

• C) $2.00

• D) $2.25

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The accompanying table shows the average salary of baseball players since 1984. Using the data in the table, create a scatter plot on the grid and state the exponential regression equation with the coefficient and base rounded to the nearest hundredth. Using your written regression equation, estimate the salary of a baseball player in the year 2005, to the nearest thousand dollars.

• $3,000,000

• $4,000,000

• $5,000,000

• $6,000,000

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The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month.

Write the exponential regression equation:

• attendance-hat = 250(1.03)^month

• attendance-hat = 250(3)^month

• attendance-hat = 250(0.97)^month

• month-hat = 250(1.03)^attendance

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