In April 2015 in the US, there was one birth every 8 seconds, one death every 12 seconds, and one new international migrant every 32 seconds. (a) Let f(t) be the population of the US, where t is time in seconds measured from the start of April 2015. Find f'(0). Give units. (b) To the nearest second, how long did it take for the US population to add one person in April 2015?

When you breathe, a muscle (called the diaphragm) reduces the pressure around your lungs and they expand to fill with air. The table shows the volume of a lung as a function of the reduction in pressure from the diaphragm. Pulmonologists (lung doctors) define the compliance of the lung as the derivative of this function.

$$\begin{matrix} \text{Pressure reduction} & \text{Volume}\\ \text{(cm of water)} & \text{(liters)}\\ \text{0} & \text{0.20}\\ \text{5} & \text{0.29}\\ \text{10} & \text{0.49}\\ \text{15} & \text{0.70}\\ \text{20} & \text{0.86}\\ \text{25} & \text{0.95}\\ \text{30} & \text{1.00}\\ \end{matrix}$$

Estimate the maximum compliance of the lung.

According to the U.S. Census Bureau, Population Division, in July 2012, there was one birth every 8 sec one death every 14 sec, and one new international migrant every 44 sec. How many seconds does it take for a net gain of one person?

Draw a coordinate plane. Then graph each point.

$$L ( 0,0 )$$

Sketch the graph of the height of a particle against time if velocity is positive and acceleration is negative.

Reread lines 91-102. In a small group, discuss the differences between the monster's appearance in the book Frankenstein and its appearance in the movie Frankenstein.

Divide, and then simplify, if possible.

$$( y + 4 ) \div \frac { y ^ { 2 } + 8 y + 16 } { a b }$$

American Airlines requires that the total outside dimensions (length+width+height) of a checked bag not exceed 62 inches. Suppose you want to check a bag whose height equals its width. What is the largest volume bag of this shape that you can check on an American flight?

The value of an automobile purchased in 2014 can be approximated by the function $V ( t ) = 30 ( 0.85 ) ^ { t },$ where t is the time, in years, from the date of purchase, and V(t) is the value, in thousands of dollars. (a) Evaluate and interpret V(4), including units. (b) Find an expression for V'(t), including units. (c) Evaluate and interpret V'(4), including units. (d) Use V(t), V'(t), and any other considerations you think are relevant to write a paragraph in support of or in opposition to the following statement: "From a monetary point of view, it is best to keep this vehicle as long as possible."

The weight, W, in lbs, of a child is a function of its age, a, in years, so W=f(a). Do you expect f'(a) to be positive or negative? Why?

Average leaf width, w (in mm), in tropical Australia is a function of the average annual rainfall, r (in mm), so w = f(r). We have f'(1500) = 0.0218. (a) What are the units of the 1500? (b) What are the units of the 0.0218? (c) About how much difference in average leaf width would you find in two forests whose average annual rainfalls are near 1500 mm but differ by 200 mm?

Suppose that f(t) is a function with f(25)=3.6 and f'(25)=-0.2. Estimate f(26) and f(30).

Two waves of the same frequency have amplitudes 1.00 and 2.00. They interfere at a point where their phase difference is 60.0°. What is the resultant amplitude?

Rik earns $\$ 18$ per hour working for Round Edge stairbuilders. How much would Rik need to earn on his own for a comparable income?