Solved: In 2011, the populations of China and India were approximately 1.34 and 1.19

Simplify the expressions in Exercises 16 completely

Simplify the expressions in Exercises 16 completely

Simplify the expressions in Exercises 16 completely

Simplify the expressions in Exercises 16 completely

Simplify the expressions in Exercises 16 completely

Simplify the expressions in Exercises 16 completely

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 718, solve for x using logs.

For Exercises 1924, solve for t. Assume a and b are positive constants and k is nonzero.

For Exercises 1924, solve for t. Assume a and b are positive constants and k is nonzero.

For Exercises 1924, solve for t. Assume a and b are positive constants and k is nonzero.

For Exercises 1924, solve for t. Assume a and b are positive constants and k is nonzero.

For Exercises 1924, solve for t. Assume a and b are positive constants and k is nonzero.

For Exercises 1924, solve for t. Assume a and b are positive constants and k is nonzero.

In Exercises 2528, put the functions in the form P = P0ekt

In Exercises 2528, put the functions in the form P = P0ekt

In Exercises 2528, put the functions in the form P = P0ekt

In Exercises 2528, put the functions in the form P = P0ekt

Find the inverse function in Exercises 2931.

Find the inverse function in Exercises 2931.

Find the inverse function in Exercises 2931.

The population of a region is growing exponentially. There were 40,000,000 people in 2000 (t = 0) and 48,000,000 in 2010. Find an expression for the population at any time t, in years. What population would you predict for the year 2020? What is the doubling time?

One hundred kilograms of a radioactive substance decay to 40 kg in 10 years. How much remains after 20 years?

A culture of bacteria originally numbers 500. After 2 hours there are 1500 bacteria in the culture. Assuming exponential growth, how many are there after 6 hours?

The population of the US was 281.4 million in 2000 and 308.7 million in 2010.23 Assuming exponential growth, (a) In what year is the population expected to go over 350 million? (b) What population is predicted for the 2020 census?

The concentration of the car exhaust fume nitrous oxide, NO2, in the air near a busy road is a function of distance from the road. The concentration decays exponentially at a continuous rate of 2.54% per meter.24 At what distance from the road is the concentration of NO2 half what it is on the road?

For children and adults with diseases such as asthma, the number of respiratory deaths per year increases by 0.33% when pollution particles increase by a microgram per cubic meter of air.25 (a) Write a formula for the number of respiratory deaths per year as a function of quantity of pollution in the air. (Let Q0 be the number of deaths per year with no pollution.) (b) What quantity of air pollution results in twice as many respiratory deaths per year as there would be without pollution?

The number of alternative fuel vehicles26 running on E85, fuel that is up to 85% plant-derived ethanol, increased exponentially in the US between 2003 and 2008. (a) Use this information to complete the missing table values. (b) How many E85-powered vehicles were there in the US in 2003? (c) By what percent did the number of E85-powered vehicles grow from 2004 to 2008?

At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by A = 10(0.82)t . (a) What was the initial amount taken? (b) What percent of the drug leaves the body each hour? (c) How much of the drug is left in the body 6 hours after the dose is administered? (d) How long is it until only 1 mg of the drug remains in the body?

A cup of coffee contains 100 mg of caffeine, which leaves the body at a continuous rate of 17% per hour. (a) Write a formula for the amount, A mg, of caffeine in the body t hours after drinking a cup of coffee. (b) Graph the function from part (a). Use the graph to estimate the half-life of caffeine. (c) Use logarithms to find the half-life of caffeine

The exponential function y(x) = Cex satisfies the conditions y(0) = 2 and y(1) = 1. Find the constants C and . What is y(2)?

Without a calculator or computer, match the functions ex, ln x, x2, and x1/2 to their graphs in Figure 1.46.

With time, t, in years since the start of 1980, textbook prices have increased at 6.7% per year while inflation has been 3.3% per year.27 Assume both rates are continuous growth rates. (a) Find a formula for B(t), the price of a textbook in year t if it cost $B0 in 1980. (b) Find a formula for P(t), the price of an item in year t if it cost $P0 in 1980 and its price rose according to inflation. (c) A textbook cost $50 in 1980. When is its price predicted to be double the price that would have resulted from inflation alone

In November 2010, a tiger summit was held in St. Petersburg, Russia.28 In 1900, there were 100,000 wild tigers worldwide; in 2010 the number was 3200. (a) Assuming the tiger population has decreased exponentially, find a formula for f(t), the number of wild tigers t years since 1900. (b) Between 2000 and 2010, the number of wild tigers decreased by 40%. Is this percentage larger or smaller than the decrease in the tiger population predicted by your answer to part (a)?

In 2011, the populations of China and India were approximately 1.34 and 1.19 billion people29, respectively. However, due to central control the annual population growth rate of China was 0.4% while the population of India was growing by 1.37% each year. If these growth rates remain constant, when will the population of India exceed that of China?

The third-quarter revenue of AppleR went from $3.68 billion30 in 2005 to $15.68 billion31 in 2010. Find an exponential function to model the revenue as a function of years since 2005. What is the continuous percent growth rate, per year, of sales?

The world population was 6.9 billion at the end of 2010 and is predicted to reach 9 billion by the end of 2050.32 (a) Assuming the population is growing exponentially, what is the continuous growth rate per year? (b) The United Nations celebrated the Day of 5 Billion on July 11, 1987, and the Day of 6 Billion on October 12, 1999. Using the growth rate in part (a), when is the Day of 7 Billion predicted to be?

In the early 1920s, Germany had tremendously high inflation, called hyperinflation. Photographs of the time show people going to the store with wheelbarrows full of money. If a loaf of bread cost 1/4 marks in 1919 and 2,400,000 marks in 1922, what was the average yearly inflation rate between 1919 and 1922?

Different isotopes (versions) of the same element can have very different half-lives. With t in years, the decay of plutonium-240 is described by the formula Q = Q0e 0.00011t , whereas the decay of plutonium-242 is described by Q = Q0e0.0000018t . Find the half-lives of plutonium-240 and plutonium-242

The size of an exponentially growing bacteria colony doubles in 5 hours. How long will it take for the number of bacteria to triple?

Air pressure, P, decreases exponentially with height, h, above sea level. If P0 is the air pressure at sea level and h is in meters, then P = P0e0.00012h. (a) At the top of Mount McKinley, height 6194 meters (about 20,320 feet), what is the air pressure, as a percent of the pressure at sea level? (b) The maximum cruising altitude of an ordinary commercial jet is around 12,000 meters (about 39,000 feet). At that height, what is the air pressure, as a percent of the sea level value?

Find the equation of the line l in Figure 1.47.

In 2010, there were about 246 million vehicles (cars and trucks) and about 308.7 million people in the US.33 The number of vehicles grew 15.5% over the previous decade, while the population has been growing at 9.7% per decade. If the growth rates remain constant, when will there be, on average, one vehicle per person?

A picture supposedly painted by Vermeer (16321675) contains 99.5% of its carbon-14 (half-life 5730 years). From this information decide whether the picture is a fake. Explain your reasoning

Is there a difference between ln[ln(x)] and ln2(x)? [Note: ln2(x) is another way of writing (ln x) 2.]

If h(x) = ln(x + a), where a > 0, what is the effect of increasing a on (a) The y-intercept? (b) The x-intercept?

If h(x) = ln(x + a), where a > 0, what is the effect of increasing a on the vertical asymptote?

If g(x) = ln(ax + 2), where a = 0, what is the effect of increasing a on (a) The y-intercept? (b) The x-intercept?

If f(x) = a ln(x + 2), what is the effect of increasing a on the vertical asymptote?

f g(x) = ln(ax + 2), where a = 0, what is the effect of increasing a on the vertical asymptote?

The function log |x| is odd.

For all x > 0, the value of ln(100x) is 100 times larger than ln x.

In Problems 6364, give an example of:

In Problems 6364, give an example of:

Are the statements in Problems 6568 true or false? Give an explanation for your answer.

Are the statements in Problems 6568 true or false? Give an explanation for your answer.

Are the statements in Problems 6568 true or false? Give an explanation for your answer.

Are the statements in Problems 6568 true or false? Give an explanation for your answer.