Exercises 51 54 present data in the form of tables. For

What was the population of Japan in 2006

What was the population of Iraq in 2006?

Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?

Which country has a decreasing population? By what percentage is the population of that country decreasing each year

When will India s population be 1238 million?

When will India s population be 1416 million?

a. In 2000, the population of Israel was approximately 6.04 million and by 2050 it is projected to grow to 10 million. Use the exponential growth model in which is the number of years after 2000, to find an exponential growth function that models the data. b. In which year will Israel s population be 9 million?

a. In 2000, the population of the Palestinians in the West Bank, Gaza Strip, and East Jerusalem was approximately 3.2 million and by 2050 it is projected to grow to 12 million. Use the exponential growth model in which is the number of years after 2000, to find the exponential growth function that models the data. b. In which year will the Palestinian population be 9 million?

In Exercises 9 14, complete the table. Round projected populations to one decimal place and values of to four decimal places

In Exercises 9 14, complete the table. Round projected populations to one decimal place and values of to four decimal places

In Exercises 9 14, complete the table. Round projected populations to one decimal place and values of to four decimal places

In Exercises 9 14, complete the table. Round projected populations to one decimal place and values of to four decimal places

In Exercises 9 14, complete the table. Round projected populations to one decimal place and values of to four decimal places

In Exercises 9 14, complete the table. Round projected populations to one decimal place and values of to four decimal places

How many grams of carbon-14 will be present in 5715 years?

How many grams of carbon-14 will be present in 11,430 years?

The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds?

The half-life of the radioactive element plutonium-239 is 25,000 years. If 16 grams of plutonium-239 are initially present, how many grams are present after 25,000 years? 50,000 years? 75,000 years? 100,000 years? 125,000 years?

Prehistoric cave paintings were discovered in a cave in France. The paint contained 15% of the original carbon-14. Estimate the age of the paintings.

Skeletons were found at a construction site in San Francisco in 1989. The skeletons contained 88% of the expected amount of carbon-14 found in a living person. In 1989, how old were the skeletons?

In Exercises 21 26, complete the table. Round half-lives to one decimal place and values of to six decimal places.

In Exercises 21 26, complete the table. Round half-lives to one decimal place and values of to six decimal places.

In Exercises 21 26, complete the table. Round half-lives to one decimal place and values of to six decimal places.

In Exercises 21 26, complete the table. Round half-lives to one decimal place and values of to six decimal places.

In Exercises 21 26, complete the table. Round half-lives to one decimal place and values of to six decimal places.

In Exercises 21 26, complete the table. Round half-lives to one decimal place and values of to six decimal places.

The August 1978 issue of National Geographic described the 1964 find of bones of a newly discovered dinosaur weighing 170 pounds, measuring 9 feet, with a 6-inch claw on one toe of each hind foot. The age of the dinosaur was estimated using potassium-40 dating of rocks surrounding the bones. a. Potassium-40 decays exponentially with a half-life of approximately 1.31 billion years. Use the fact that after 1.31 billion years a given amount of potassium-40 will have decayed to half the original amount to show that the decay model for potassium-40 is given by where is in billions of years. b. Analysis of the rocks surrounding the dinosaur bones indicated that 94.5% of the original amount of potassium-40 was still present. Let in the model in part (a) and estimate the age of the bones of the dinosaur.

The half-life of thorium-229 is 7340 years. How long will it take for a sample of this substance to decay to 20% of its original amount?

The half-life of lead is 22 years. How long will it take for a sample of this substance to decay to 80% of its original amount?

The half-life of aspirin in your bloodstream is 12 hours. How long will it take for the aspirin to decay to 70% of the original dosage

Xanax is a tranquilizer used in the short-term relief of symptoms of anxiety. Its half-life in the bloodstream is 36 hours. How long will it take for Xanax to decay to 90% of the original dosage?

A bird species in danger of extinction has a population that is decreasing exponentially Five years ago the population was at 1400 and today only 1000 of the birds are alive. Once the population drops below 100, the situation will be irreversible. When will this happen?

Use the exponential growth model, to show that the time it takes a population to double (to grow from to ) is given by

Use the exponential growth model, to show that the time it takes a population to triple (to grow from to ) is given by

The growth model describes New Zealand s population, in millions, years after 2006. a. What is New Zealand s growth rate? b. How long will it take New Zealand to double its population?

The growth model describes Mexico s population, in millions, years after 2006. a. What is Mexico s growth rate? b. How long will it take Mexico to double its population?

The logistic growth function describes the number of people, who have become ill with influenza weeks after its initial outbreak in a particular community. a. How many people became ill with the flu when the epidemic began? b. How many people were ill by the end of the fourth week? c. What is the limiting size of the population that becomes ill?

How well does the function model the data for 2000?

How well does the function model the data for 2006?

When will world population reach 7 billion?

When will world population reach 8 billion?

According to the model, what is the limiting size of the population that Earth will eventually sustain?

What percentage of 20-year-olds have some coronary heart disease?

What percentage of 80-year-olds have some coronary heart disease?

At what age is the percentage of some coronary heart disease 50%?

At what age is the percentage of some coronary heart disease 70%?

A bottle of juice initially has a temperature of 70F. It is left to cool in a refrigerator that has a temperature of 45F. After 10 minutes, the temperature of the juice is 55F. a. Use Newton s Law of Cooling to find a model for the temperature of the juice, after minutes. b. What is the temperature of the juice after 15 minutes? c. When will the temperature of the juice be 50F?

A pizza removed from the oven has a temperature of 450F. It is left sitting in a room that has a temperature of 70F. After 5 minutes, the temperature of the pizza is 300F. a. Use Newton s Law of Cooling to find a model for the temperature of the pizza, after minutes. b. What is the temperature of the pizza after 20 minutes? c. When will the temperature of the pizza be 140F?

A frozen steak initially has a temperature of 28F. It is left to thaw in a room that has a temperature of 75F. After 10 minutes, the temperature of the steak has risen to 38F. After how many minutes will the temperature of the steak be 50F?

A frozen steak initially has a temperature of 24F. It is left to thaw in a room that has a temperature of 65F. After 10 minutes, the temperature of the steak has risen to 30F. After how many minutes will the temperature of the steak be 45F?

Exercises 51 54 present data in the form of tables. For each data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. (If applicable, in Exercise 74, you will use your graphing utility to obtain these functions.)

Exercises 51 54 present data in the form of tables. For each data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. (If applicable, in Exercise 74, you will use your graphing utility to obtain these functions.)

Exercises 51 54 present data in the form of tables. For each data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. (If applicable, in Exercise 74, you will use your graphing utility to obtain these functions.)

Exercises 51 54 present data in the form of tables. For each data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. (If applicable, in Exercise 74, you will use your graphing utility to obtain these functions.)

In Exercises 55 58, rewrite the equation in terms of base Express the answer in terms of a natural logarithm and then round to three decimal places

In Exercises 55 58, rewrite the equation in terms of base Express the answer in terms of a natural logarithm and then round to three decimal places

In Exercises 55 58, rewrite the equation in terms of base Express the answer in terms of a natural logarithm and then round to three decimal places

In Exercises 55 58, rewrite the equation in terms of base Express the answer in terms of a natural logarithm and then round to three decimal places

Nigeria has a growth rate of 0.025 or 2.5%. Describe what this means

How can you tell whether an exponential model describes exponential growth or exponential decay?

Suppose that a population that is growing exponentially increases from 800,000 people in 2003 to 1,000,000 people in 2006.Without showing the details, describe how to obtain the exponential growth function that models the data.

What is the half-life of a substance?

Describe a difference between exponential growth and logistic growth.

Describe the shape of a scatter plot that suggests modeling the data with an exponential function

You take up weightlifting and record the maximum number of pounds you can lift at the end of each week. You start off with rapid growth in terms of the weight you can lift from week to week, but then the growth begins to level off. Describe how to obtain a function that models the number of pounds you can lift at the end of each week. How can you use this function to predict what might happen if you continue the sport?

Would you prefer that your salary be modeled exponentially or logarithmically? Explain your answer

One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population

a. Use your graphing utility s exponential regression option to obtain a model of the form that fits the data. How well does the correlation coefficient, indicate that the model fits the data? b. Rewrite the model in terms of base By what percentage is the population of the United States increasing each year?

Use your graphing utility s logarithmic regression option to obtain a model of the form that fits the data. How well does the correlation coefficient, indicate that the model fits the data?

Use your graphing utility s linear regression option to obtain a model of the form that fits the data. How well does the correlation coefficient, indicate that the model fits the data?

Use your graphing utility s power regression option to obtain a model of the form that fits the data. How well does the correlation coefficient, indicate that the model fits the data?

Use the values of in Exercises 68 71 to select the two models of best fit. Use each of these models to predict by which year the U.S. population will reach 315 million. How do these answers compare to the year we found in Example 1, namely 2010? If you obtained different years, how do you account for this difference?

The figure shows the number of people in the United States age 65 and over, with projected figures for the year 2010 and beyond

In Exercises 51 54, you determined the best choice for the kind of function that modeled the data in the table. For each of the exercises that you worked, use a graphing utility to find the actual function that best fits the data. Then use the model to make a reasonable prediction for a value that exceeds those shown in the table s first column.

I used an exponential model with a positive growth rate to describe the depreciation in my car s value over four years.

After 100 years, a population whose growth rate is 3% will have three times as many people as a population whose growth rate is 1%.

When I used an exponential function to model Russia s declining population, the growth rate was negative.

Because carbon-14 decays exponentially, carbon dating can determine the ages of ancient fossils.

In 2006, Canada s population exceeded Uganda s by 4.9 million

By 2009, the models indicate that Canada s population will exceed Uganda s by approximately 2.8 million.

The models indicate that in 2013, Uganda s population will exceed Canada s.

Uganda s growth rate is approximately 3.8 times that of Canada s.

Use Newton s Law of Cooling, to solve this exercise. At 9:00 A.M., a coroner arrived at the home of a person who had died during the night. The temperature of the room was 70F, and at the time of death the person had a body temperature of 98.6F. The coroner took the body s temperature at 9:30 A.M., at which time it was 85.6F, and again at 10:00 A.M., when it was 82.7F. At what time did the person die?

Each group member should consult an almanac, newspaper, magazine, or the Internet to find data that can be modeled by exponential or logarithmic functions. Group members should select the two sets of data that are most interesting and relevant. For each set selected, find a model that best fits the data. Each group member should make one prediction based on the model and then discuss a consequence of this prediction. What factors might change the accuracy of the prediction?

Exercises 85 87 will help you prepare for the material covered in the first section of the next chapter.

Exercises 85 87 will help you prepare for the material covered in the first section of the next chapter.

Exercises 85 87 will help you prepare for the material covered in the first section of the next chapter.