The function $P(t)=145 e^{-0.092 t}$ models a runner's pulse, $P(t)$, in beats per minute, $t$ minutes after a race, where $0 \leq t \leq 15$. Graph the function using a graphing utility. $\boxed{\text{TRACE}}$ along the graph and determine after how many minutes the runner's pulse will be $70$ beats per minute. Round to the nearest tenth of a minute. Verify your observation algebraically.

(II) A source emits sound of wavelengths $2.64 \mathrm{~m}$ and $2.72 \mathrm{~m}$ in air. (a) How many beats per second will be heard? (Assume $T=20^{\circ} \mathrm{C}$.)

A string on a guitar vibrates with a frequency of 440 Hz. Two beats are heard when this string and a string on another guitar are played at the same time. What are the possible frequencies of vibration of the second string?

Recommended heart rates during exercise vary with age and physical condition. For a healthy person doing moderate to intense exercise, such as hiking, the inequality $0.5(220-a) \leq R \leq 0.9(220-a)$ gives a target range for the heart rate R (in beats per minute), based on age a (in years). a. What is the target range for heart rates for a person 15 years old? b. How old is a person whose target range is between 99 and 178.2 beats per minute?

Recommended heart rates during exercise vary with age and physical condition. For a healthy person doing moderate to intense exercise, such as hiking. the inequality

$$0.5 ( 220 - a ) \leq R \leq 0.9 ( 220 - a )$$

gives a target range for the heart rate R (in beats per minute), based on age a (in years). a. What is the target range for heart rates for a person 15 years old? b. How old is a person whose target range is between 99 and 178.2 beats per minute?

Five pulse rates randomly selected and have a mean of 78.0 beats per minute. Four of the pulse rates are 82, 78, 56, and 84.Find the mis ing value.

Show that in a tournament (defined preceding mentioned theorem) it is always possible to rank the contestants so that the person ranked ith beats the person ranked (i +1)st. (Hint: Use the mentioned theorem.)

Your heart beats about 72 times per minute. At that rate how many times will it beat in one hour? (Write an equation and solve the problem.)

Find mean, median, mode, and range. Which measure best describes each group of data? Explain. resting heart rate in beats per minute: 79 72 80 81 40 72

You heart beats about 72 times per minute. At that rate, how many times will it beat in one hour? (Write an equation and solve the problem.)

A police siren contains two frequencies, producing a wavering sound (beats). Explain how the siren sound changes as a police car approaches, passes, and moves away from a pedestrian.

Why do you think Neruda calls the "constancy that beats in your chest" (literally, his beloved's heartbeat) a "purer motion"? Interpret the remarkable visual image in line $11$.

To play a $\mathrm{C}$ major chord on the piano, you hit the $\mathrm{C}, \mathrm{E}$, and $\mathrm{G}$ keys simultaneously. When you do so, you hear no beats. Why?

A police siren contains at least two frequencies, producing the wavering sound (beats). Explain how the siren sound changes as a police car approaches, passes, and moves away from a pedestrian.