Chapter 8

Then evaluate the expression when \(a=1\) and \(b=2\). $$ -\left(a b^{3}\right)^{2} $$

Sketch the graphs of \(y=2^{x}\) and \(y=\left(\frac{1}{2}\right)^{x} .\) How are the graphs related?

You roll a die six times. What is the probability that you will roll six even numbers in a row?

In Exercises \(58-60\), use the following information. In \(1803,\) the Louisiana Purchase added \(8.28 \times 10^{5}\) square miles to the United States. The cost of this land was \(\$ 15\) million. In \(1853,\) the Gadsden Purchase added \(2.94 \times 10^{4}\) square miles, and the cost was \(\$ 10\) million. WATERFALL Stanley Falls in Congo, Africa, has an average flow of about \(1.7 \times 10^{4}\) cubic meters per second. How much water goes over Stanley Falls in a typical 30-day month?

You work for a real estate company that wants to build a new apartment complex. A team is formed to decide in which state to build the complex. One team member wants to build in Arizona. Another team member wants to build in Michigan. Your boss asks you to decide where to build the complex. You find that the population \(P\) of Arizona (in thousands) in 1995 projected through 2025 can be modeled by \(P=4264(1.0208)^{t},\) where \(t=0\) represents \(1995 .\) Find the ratio of the population in 2025 to the population in 2000 .

In Exercises \(58-60\), use the following information. In \(1803,\) the Louisiana Purchase added \(8.28 \times 10^{5}\) square miles to the United States. The cost of this land was \(\$ 15\) million. In \(1853,\) the Gadsden Purchase added \(2.94 \times 10^{4}\) square miles, and the cost was \(\$ 10\) million. C. HEARTBEATS Consider a person whose heart beats 70 times per minute and who lives to be 85 years old. Estimate the number of times the person's heart beats during his or her life. Do not acknowledge leap years. Write your answer in decimal form and in scientific notation.

Complete the statement using \(>\) or \(<\). $$(5 \cdot 6)^{4} \underline{?} 5 \cdot 6^{4}$$

What point do all graphs of the form \(y=a^{x}\) have in common? Is there a point that all graphs of the form \(y=2(a)^{x}\) have in common? If so, name the point.

You work for a real estate company that wants to build a new apartment complex. A team is formed to decide in which state to build the complex. One team member wants to build in Arizona. Another team member wants to build in Michigan. Your boss asks you to decide where to build the complex. You find that the population \(P\) of Michigan (in thousands) in 1995 projected through 2025 can be modeled by \(P=9540(1.0026)^{t},\) where \(t=0\) represents \(1995 .\) Find the ratio of the population in 2025 to the population in \(2000 .\)

Complete the statement using \(>\) or \(<\). $$5^{2} \cdot 3^{6} \underline{?}(5 \cdot 3)^{6}$$

You started a savings account in \(1990 .\) The balance \(A\) is modeled by \(A=450(1.06)^{t},\) where \(t=0\) represents the year \(2000 .\) What is the balance in the account in \(1990 ?\) in \(2000 ?\) in \(2010 ?\)

MULTIPLE CHOICE Which number is not in scientific notation? $$ \begin{array}{lllll} \text { (A) } 1 \times 10^{4} & \text { (B) } 3.4 \times 10^{-3} & \text { (C) } 9.02 \times 10^{2} & \text { (D) } 12.25 \times 10^{-5} \end{array} $$

Complete the statement using \(>\) or \(<\). $$\left(3^{6} \cdot 3^{12}\right) \geq 3^{72}$$

MULTIPLE CHOICE Evaluate \(\frac{1.1 \times 10^{-1}}{5.5 \times 10^{-5}}\) using scientific notation. $$ \begin{array}{lll} \text { (A) } 0.2 \times 10^{-4} & \text { (B) } 2.0 \times 10^{4} \end{array} $$ $$ \begin{array}{llll} \text { (C) } & 2.0 \times 10^{3} & \text { (D) } 0.2 \times 10^{4} \end{array} $$

Complete the statement using \(>\) or \(<\). $$ 4^{2} \cdot 4^{8} \underline{?} 4^{16} $$

A piece of notebook paper is about 0.0032 inch thick. If you begin with a stack consisting of a single sheet and double the stack 25 times, how tall will the stack be in inches? How tall will it be in feet? (Hint: Write and solve an exponential equation to find the height of the stack in inches. Then use unit analysis to find the height in feet.)

Complete the statement using \(>\) or \(<\). $$ \left(7^{2}\right)^{3} \geq 7^{5} $$

Evaluate the expression. $$ 10^{5} $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 22 \% $$

Complete the statement using \(>\) or \(<\). $$ \left(6^{2} \cdot 3\right)^{3} \geq 6^{5} \cdot 3^{3} $$

Evaluate the expression. $$ 10^{3} $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 87.5 \% $$

Simplify the expression. Then use a calculator to evaluate the expression. Round the result to the nearest tenth when appropriate. $$ (2.1 \cdot 4.4)^{3} $$

Evaluate the expression. $$ 10^{-4} $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 0.07 \% $$

Simplify the expression. Then use a calculator to evaluate the expression. Round the result to the nearest tenth when appropriate. $$ 6.5^{3} \cdot 6.5^{4} $$

Suppose you did not know that for \(b \neq 0, b^{0}=1 .\) Based on the equation \(b^{2} \cdot b^{0}=b^{2+0}=b^{2},\) explain why you might want to make this definition.

Evaluate the expression. $$ 10^{-8} $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 8.42 \% $$

Simplify the expression. Then use a calculator to evaluate the expression. Round the result to the nearest tenth when appropriate. $$ 2.6^{4} \cdot 2.6^{2} $$

Evaluate the expression. $$\left(\frac{2}{5}\right)^{2}$$

Sketch the graph of the inequality in a coordinate plane. $$ x \geq 5 $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ \frac{1}{2} \% $$

Simplify the expression. Then use a calculator to evaluate the expression. Round the result to the nearest tenth when appropriate. $$ (5.0 \cdot 4.9)^{2} $$

Evaluate the expression. $$\left(\frac{1}{2}\right)^{3}$$

Sketch the graph of the inequality in a coordinate plane. $$ x+3<4 $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ \frac{3}{4} \% $$

Simplify the expression. Then use a calculator to evaluate the expression. Round the result to the nearest tenth when appropriate. $$ \left(3.7^{3}\right)^{5} $$

Evaluate the expression. $$\left(-\frac{9}{10}\right)^{3}$$

Sketch the graph of the inequality in a coordinate plane. $$ y>-2 $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 255 \% $$

Simplify the expression. Then use a calculator to evaluate the expression. Round the result to the nearest tenth when appropriate. $$ \left(8.4^{2}\right)^{4} $$

Evaluate the expression. $$\left(\frac{1}{5}\right)^{4}$$

Sketch the graph of the inequality in a coordinate plane. $$ y \leq-1.5 $$

PERCENTS AS DECIMALS Write the percent as a decimal. $$ 1 \frac{1}{4} \% $$

Solve the inequality. Then sketch a graph of the solution on a number line. $$|5+x|+4 \leq 11$$

Sketch the graph of the inequality in a coordinate plane. $$ x \geq 2.5 $$

GRAPHING LINEAR SYSTEMS Use the graphing method to solve the linear system and describe its solution(s). $$ \begin{aligned} &4 x+2 y=12\\\ &-6 x+3 y=6 \end{aligned} $$

Solve the inequality. Then sketch a graph of the solution on a number line. $$|3 x+7|-4>9 \quad $$

Sketch the graph of the inequality in a coordinate plane. $$ 3 x-y<0 $$