## Algebra and Trigonometry

Mathematics

## Quiz 5 :

Inverse, Exponential, and Logarithmic Functions

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Q03 Q03 Q03

Ventilation is an effective way to improve indoor air quality. In nonsmoking restaurants, air circulation requirements (in ) are given by the function , where x is the number of people in the dining area. Find . Use to determine the maximum number of people that should be in a restaurant having a ventilation capability of 2,700 .

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Q13 Q13 Q13

In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is usually assumed that the number of fish N( t ) still alive after t years is given by an exponential function. For Pacific halibut, , where N

_{ o }is the initial size of the cohort. Approximate the percentage of the original number still alive after 9 years.Free

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Q16 Q16 Q16

An urban density model is a formula that relates the population density D ( in thousands/ mi

^{ 2 }) to the distance x (in miles) from the center of the city. The formula for the central density a and coefficient of decay b has been found to be appropriate for many large U.S. cities. For the city of Atlanta in 1970, a = 5.5 and b = 0.10. At approximately what distance was the population density 2,800 per square mile?Free

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Q20 Q20 Q20

If the pollution of Lake Erie were stopped suddenly, it has been estimated that the level y of pollutants would decrease according to the formula y = y

_{ o }e^{ -0.3937}^{t}^{ }, where t is the time in years and y_{ o }is the pollutant level at which further pollution ceased. How many years would it take to clear 59% of the pollutants?Free

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Q21 Q21 Q21

One method of estimating the thickness of the ozone layer is to use the formula , where I

_{ o }is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, and k is the absorption constant of ozone for that wavelength. Suppose a wavelength of cm with k = 0.43 , is measured as 1.17. Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.Free

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Q27 Q27 Q27

Ventilation is an effective way to improve indoor air quality. In nonsmoking restaurants, air circulation requirements (in ) are given by the function , where x is the number of people in the dining area. Find . Use to determine the maximum number of people that should be in a restaurant having a ventilation capability of 2,550 .

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Q37 Q37 Q37

In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is usually assumed that the number of fish N( t ) still alive after t years is given by an exponential function. For Pacific halibut, , where N

_{ o }is the initial size of the cohort. Approximate the percentage of the original number still alive after 14 years.Free

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Q40 Q40 Q40

An urban density model is a formula that relates the population density D ( in thousands/ mi

^{ 2 }) to the distance x (in miles) from the center of the city. The formula for the central density a and coefficient of decay b has been found to be appropriate for many large U.S. cities. For the city of Atlanta in 1970, a = 5.5 and b = 0.10. At approximately what distance was the population density 1,800 per square mile?Free

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Q44 Q44 Q44

If the pollution of Lake Erie were stopped suddenly, it has been estimated that the level y of pollutants would decrease according to the formula y = y

_{ o }e^{ -0.3937}^{t}^{ }, where t is the time in years and y_{ o }is the pollutant level at which further pollution ceased. How many years would it take to clear 59% of the pollutants?Free

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Q45 Q45 Q45

One method of estimating the thickness of the ozone layer is to use the formula , where I

_{ o }is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, and k is the absorption constant of ozone for that wavelength. Suppose a wavelength of cm with k = 0.45 , is measured as 1.14. Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.Free

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Q51 Q51 Q51

Ventilation is an effective way to improve indoor air quality. In nonsmoking restaurants, air circulation requirements (in ) are given by the function , where x is the number of people in the dining area. Find . Use to determine the maximum number of people that should be in a restaurant having a ventilation capability of 2,350 .

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Q61 Q61 Q61

In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is usually assumed that the number of fish N( t ) still alive after t years is given by an exponential function. For Pacific halibut, , where N

_{ o }is the initial size of the cohort. Approximate the percentage of the original number still alive after 7 years.Free

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Q64 Q64 Q64

An urban density model is a formula that relates the population density D ( in thousands/ mi

^{ 2 }) to the distance x (in miles) from the center of the city. The formula for the central density a and coefficient of decay b has been found to be appropriate for many large U.S. cities. For the city of Atlanta in 1970, a = 5.5 and b = 0.10. At approximately what distance was the population density 800 per square mile?Free

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Q68 Q68 Q68

If the pollution of Lake Erie were stopped suddenly, it has been estimated that the level y of pollutants would decrease according to the formula y = y

_{ o }e^{ -0.3937}^{t}^{ }, where t is the time in years and y_{ o }is the pollutant level at which further pollution ceased. How many years would it take to clear 59% of the pollutants?Free

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Q69 Q69 Q69

One method of estimating the thickness of the ozone layer is to use the formula , where I

_{ o }is the intensity of a particular wavelength of light from the sun before it reaches the atmosphere, I is the intensity of the same wavelength after passing through a layer of ozone x centimeters thick, and k is the absorption constant of ozone for that wavelength. Suppose a wavelength of cm with k = 0.36 , is measured as 1.12. Approximate the thickness of the ozone layer to the nearest 0.01 centimeter.Free

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Q80 Q80 Q80

Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula: where k = [1 + ( r / 12 )]

^{ 12}^{t}^{ }and t is the number of years that the loan is in effect. An automobile dealer offers customers no-down-payment 7-year loans at an interest rate of 7%. If a customer can afford to pay $108 per month, find the price of the most expensive car that can be purchased.Free

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Q81 Q81 Q81

In 1980, the population of blue whales in the southern hemisphere was thought to number 5,000. The population N(t) has been decreasing according to the formula where t is in years and t = 0 corresponds to 1980. Predict the population in the year 2015 if this trend continues.

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Q104 Q104 Q104

Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula: where k = [1 + ( r / 12 )]

^{ 12}^{t}^{ }and t is the number of years that the loan is in effect. An automobile dealer offers customers no-down-payment 4-year loans at an interest rate of 15%. If a customer can afford to pay $229 per month, find the price of the most expensive car that can be purchased.Free

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Q105 Q105 Q105

In 1980, the population of blue whales in the southern hemisphere was thought to number 5,000. The population N(t) has been decreasing according to the formula where t is in years and t = 0 corresponds to 1980. Predict the population in the year 2020 if this trend continues.

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Q128 Q128 Q128

Some lending institutions calculate the monthly payment M on a loan of L dollars at an interest rate r (expressed as a decimal) by using the formula: where k = [1 + ( r / 12 )]

^{ 12}^{t}^{ }and t is the number of years that the loan is in effect. An automobile dealer offers customers no-down-payment 8-year loans at an interest rate of 10%. If a customer can afford to pay $122 per month, find the price of the most expensive car that can be purchased.Free

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Q129 Q129 Q129

In 1980, the population of blue whales in the southern hemisphere was thought to number 5,000. The population N(t) has been decreasing according to the formula where t is in years and t = 0 corresponds to 1980. Predict the population in the year 2010 if this trend continues.

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