An investment of $\$5000$ doubles in value every decade. The function $f(x)=5000\cdot 2^x$, where $x$ is the number of decades, models the growth of the value of the investment. How much is the investment worth after $30$ yr?

Find the general solution of the given system.

$$\mathbf{X}^{\prime}=\left(\begin{array}{rr}{12} & {-9} \\ {4} & {0}\end{array}\right) \mathbf{X}$$

What are some examples of symbols in 1984 and how to interpret them?

Solve each problem, and express the answer in scientific notation. a. $\left(4 \times 10^{2}\right) \times\left(1 \times 10^{8}\right)$ b. $\left(2 \times 10^{-4}\right) \times\left(3 \times 10^{2}\right)$ c. $\left(6 \times 10^{2}\right) \div\left(2 \times 10^{\prime}\right)$ d. $\left(8 \times 10^{4}\right) \div\left(4 \times 10^{1}\right)$

Determine which numbers are (a) natural numbers, (b) whole numbers, (c) integers, (d) rational numbers, and (e) irrational numbers. $\left\{-9,-\frac{7}{2}, 5, \frac{2}{3}, \sqrt{2}, 0,1,-4,-1\right\}$

Write an equation of the line through the given points. (0, 4), (3, 3)

describe how to transform the graph of y =ln x into the graph of the given function. Sketch the graph by hand and support your sketch with a grapher.

$$f(x)=ln(2-x)$$

Find $(f \cdot g)(-2)$ for the following functions.

$$\begin{array}{l}{f(x)=-x^{2}+2 x-2} \\ {g(x)=2 x+3}\end{array}$$

A. -20 B. 8 C. 120 D. 215

Order the functions from narrowest graph to widest.

$$f ( x ) = x ^ { 2 } , g ( x ) = - \frac { 4 } { 5 } x ^ { 2 }$$

,

$$h ( x ) = 3 x ^ { 2 }$$

Let

$$F _ { 1 } \left( y _ { 1 } \right) \text { and } F _ { 2 } \left( y _ { 2 } \right)$$

be two distribution functions. For any

$$\alpha , - 1 \leq \alpha \leq 1$$

, consider

$$Y _ { 1 }$$

and

$$Y _ { 2 }$$

with joint distribution function

$$F \left( y _ { 1 } , y _ { 2 } \right) = F _ { 1 } \left( y _ { 1 } \right) F _ { 2 } \left( y _ { 2 } \right) \left[ 1 - \alpha \left\{ 1 - F _ { 1 } \left( y _ { 1 } \right) \right\} \left\{ 1 - F _ { 2 } \left( y _ { 2 } \right) \right\} \right]$$

. What is

$$F \left( y _ { 1 } , \infty \right)$$

, the marginal distribution function of

$$Y _ { 1 }$$

? [Hint: What is

$$F _ { 2 } ( \infty )$$

?]

In one year, there were 116 homicide deaths in Richmond, Virginia. For a randomly selected day, find the probability that the number of homicide deaths is 0. Compare the calculated probabilities to these actual results: 268 days (no homicides); 79 days (1 homicide); 17 days (2 homicides); 1 day (3 homicides); no days with more than 3 homicides.

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. Identify any asymptotes of the graph. $f(x)=e^{-x}$

What can you tell about the character of the speaker in "Rice and Rose Bowl Blues"?

If

$$180 ^ { \circ } < \theta < 360 ^ { \circ }$$

, and

$$\cos \theta = - \frac { 21 } { 29 }$$

, find the following: cos 2

$$\theta$$