Use the radiometric dating formula to answer the following question. Uranium- $238$ has a half-life of $4.5$ billion years. a. You find a rock containing a mixture of uranium-$238$ and lead. You determine that $60 \%$ of the original uranium- $238$ remains; the other $40 \%$ decayed into lead. How old is the rock? b. Analysis of another rock shows that it contains $55 \%$ of its original uranium-$238$; the other $45 \%$ decayed into lead. How old is the rock?

On previous page , we noted that the growth rate of per capita GDP in the United States between $1870$ and $1929$ was slightly lower than $2.0 \%$, while the growth rate between $1950$ and $2015$ was slightly higher. Using the following table, calculate the actual average annual growth rates during these two periods.

The pain-killer oxycodone is eliminated from the blood stream exponentially with a half-life of $3.5$ hours. Assume that a patient receives an initial dose of $10$ milligrams of oxycodone at noon. a. How much oxycodone is in the patient's blood at $6:00$ p.m. the same day? b. Estimate when the oxycodone concentration will reach $10 \%$ of its initial level.

In $1923$, Germany underwent one of the worst periods in history of hyperinflation extraordinarily large inflation in prices. At its peak, prices rose $30,000 \%$ per month. At this rate, by what percentage would prices have risen in $1$ year? in $1$ day?

For the following function involving the variables listed, use your intuition or additional research, if necessary, to do the following. a. Describe an appropriate domain and range for the function. b. Make a rough sketch of a graph of the function. Explain the assumptions that go into your sketch. c. Briefly discuss the validity of your graph as a model of the true function. (weight of car, average gas mileage)

The pressure of Earth's atmosphere at sea level is approximately $1000$ millibars (mb), and it decreases by a factor of $2$ for every $7$ kilometers of increase in altitude. a. If you live at an elevation of $1$ kilometer (roughly $3300$ feet), what is the atmospheric pressure? b. What is the atmospheric pressure at the top of Mount Everest (elevation of $8848$ meters)? c. By approximately what percentage does atmospheric pressure decrease every kilometer?

The pressure of Earth’s atmosphere at sea level is approximately 1000 millibars and decreases exponentially with elevation. At an elevation of 30,000 ft (approximately the altitude of Mt. Everest), the pressure is one-third the sea-level pressure. At what elevation is the pressure half the sea-level pressure? At what elevation is it 1% of the sea-level pressure?

For the following functions find out the slope of the graph and the intercept. Then sketch the graph for values of $x$ between $-10$ and 10 .

$$y=2 x+4$$

a. The decibel level for busy street traffic in Table $8.5$ is based on the assumption that you stand very close to the noise source-say, $1$ meter from the street. If your house is $100$ meters from a busy street, how loud will the street noise be, in decibels? b. At a distance of $10$ meters from the speakers at a concert, the sound level is $135$ decibels. How far away should you sit to reduce the level to $120$ decibels? c. Imagine that you are a spy in a restaurant. The conversation you want to hear is taking place in a booth across the room, about $8$ meters away. The people are speaking softly, so they hear each other's voice at about $20$ decibels (they are sitting about $1$ meter apart). How loud is the sound of their voices when it reaches your table? If you have a miniature amplifier in your ear and want to hear their voices at $60$ decibels, by what factor must you amplify their voices?

Suppose that for the average individual, aspirin has a half-life of $8$ hours in the bloodstream. At $12:00$ noon, you take a $300$ -milligram dose of aspirin. a. How much aspirin will be in your blood at $6: 00$ p.m. the same day? At midnight? At $12:00$ noon the next day? b. Estimate when the amount of aspirin will decay to $5 \%$ of its original amount.

Briefly explain how repeated doublings characterize exponential growth. Describe the impact of doublings, using the chessboard or magic penny parable.

Use the magic penny parable presented in the text.

How much money would you have after $22$ days?

By using the magic penny parable presented in the text. How much money would you have after $21$ days?

Decide whether the following statement is true or false. Explain your reasoning. Our town is growing with a doubling time of $25$ years, so its population will triple in $50$ years.