Give an answer for the following questions.

(a) What is the wavelength of a photon whose momentum is equal to that of an electron with a speed of $2000 \mathrm{~m} / \mathrm{s}$ ?

(b) What is the ratio of their energies?

A farm purchased in 2000 for $1,000,000 was valued at$3 million in 2010. If the farm continues to appreciate at the same rate (with continuous compounding), when will it be worth $10 million?

Compute the total and annual returns on the following investments.

Three years after paying $\$ 3500$ for shares in a startup company, you sell the shares for $\$ 2000$ (at a loss).

Let P(t) be the population, in thousands, of a city t years after January 1, 2000. Interpret the equation $P(8)=64.3$. What does $P(4.5)$ represent?

The population of Texas from 1950 to 2000 is shown in the table below.

$$\begin{matrix} \text{Year} & \text{Resident Population}\\ \text{1950} & \text{7,711,194}\\ \text{1960} & \text{9,579,677}\\ \text{1970} & \text{11,198,655}\\ \text{1980} & \text{14,225,513}\\ \text{1990} & \text{16,986,510}\\ \text{2000} & \text{20,851,820}\\ \end{matrix}$$

Is the function a good fit for the data? Why or why not?

As we mentioned earlier in this section, we stopped the t-table at df=2000 and supplied the corresponding values of $z _\alpha$ beneath. Explain why that makes sense.

Calculate the solution to $1000 \ddot{x}(t)+200 \dot{x}(t)+2000 x(t)=100 \delta(t), x_{0}=0, v_{0}=0$

The table shows the census population $y$ (in millions) of the United States for each census year $x$ from 1950 to 2000.

$$\begin{array}{|c|c|} \hline \text { Year, } \boldsymbol{x} & \text { Population, } \boldsymbol{y} \\ \hline 1950 & 151.33 \\ 1960 & 179.32 \\ 1970 & 203.30 \\ 1980 & 226.54 \\ 1990 & 248.72 \\ 2000 & 281.42 \\ \hline \end{array}$$

Find the percent increase in population from each census year to the next.

The total sales (in millions of dollars) for Barnes & Noble from 1992 to 2000 are listed below.

$$\begin{array}{llllll}1992 & 1086.7 & 1995 & 1976.9 & 1998 & 3005.6 \\ 1993 & 1337.4 & 1996 & 2448.1 & 1999 & 3486.0 \\ 1994 & 1622.7 & 1997 & 2796.8 & 2000 & 4375.8\end{array}$$

Compare the linear model you found in part (b) with the linear model given by the graphing utility in part (c).

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Yesterday I drank 2000

$$cm^3$$

of water.

The table shows the census population $y$ (in millions) of the United States for each census year $x$ from 1950 to 2000.

$$\begin{array}{|c|c|} \hline \text { Year, } \boldsymbol{x} & \text { Population, } \boldsymbol{y} \\ \hline 1950 & 151.33 \\ 1960 & 179.32 \\ 1970 & 203.30 \\ 1980 & 226.54 \\ 1990 & 248.72 \\ 2000 & 281.42 \\ \hline \end{array}$$

Sketch a scatter plot of the data. Describe any trends in the data.

Suppose $f(x)=100 x^2-5 x$ thousand units are produced, where x is the number of years after 2000. How many units are produced in 2010, according to this function?

The table gives the US midyear population, in millions, from 1990 to 2010. If P(t) is the population at time t, estimate and interpret the value of the derivative P'(2000).

$$\begin{matrix} \text{t} & \text{1990} & \text{1995} & \text{2000} & \text{2005} & \text{2010}\\ \text{P(t)} & \text{249.6} & \text{266.3} & \text{282.2} & \text{295.8} & \text{308.3}\\ \end{matrix}$$

Which of the following years had the greatest increase in amount of material recycled?

A. 2000-2001

C. $1996-1997$

B. $1998-1999$

D. $1995-1996$