Chapter 8

Classify the model as exponential growth or exponential decay. Then identify the growth or decay factor and graph the model. $$ y=9\left(\frac{2}{5}\right)^{t} $$

Solve the equation. (Lesson 3.5) $$-2(4-3 x)=6(2 x+1)+4$$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \left(9 \times 10^{-6}\right)\left(2 \times 10^{4}\right) $$

Using your graphs , describe the domain and the range of the function. $$y=-5\left(\frac{1}{5}\right)^{x}$$

Copy and complete the statement using \(<\) or \(>\). \((3 \cdot 2)^{6} ?\left(3^{2}\right)^{6}\)

Classify the model as exponential growth or exponential decay. Then identify the growth or decay factor and graph the model. $$ y=35\left(\frac{5}{4}\right)^{t} $$

Solve the equation. (Lesson 3.5) $$7 x-(4 x+3)=4(3 x+15)$$

Simplify the expression. Use only positive exponents. $$ \frac{4 x^{3} y^{3}}{2 x y} \cdot \frac{5 x y^{2}}{2 y} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \left(6 \times 10^{5}\right)\left(2.5 \times 10^{-1}\right) $$

Copy and complete the statement using \(<\) or \(>\). \(4^{2} \cdot 4^{8} ?(4 \cdot 4)^{10}\)

Using your graphs , describe the domain and the range of the function. $$y=2\left(\frac{2}{3}\right)^{x}$$

Use a calculator to investigate the effects of a and b on the graph of \(y=a b^{x}\) In the same viewing rectangle, graph \(y=2(2)^{x}, y=4(2)^{x},\) and \(y=8(2)^{x}\) How does an increase in the value of \(a\) affect the graph of \(y=a b^{x} ?\)

Solve the equation. (Lesson 3.5) $$\frac{2}{3}(6 m-3)+10=-8(m+2)$$

Simplify the expression. Use only positive exponents. $$ \frac{16 x^{3} y}{-4 x y^{3}} \cdot \frac{-2 x y}{x} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \frac{8 \times 10^{-3}}{4 \times 10^{-5}} $$

Copy and complete the statement using \(<\) or \(>\). \(7^{3} \cdot 7^{4} \quad ? \quad(7 \cdot 7)^{4}\)

Rewrite the expression with positive exponents. $$ x^{-5} $$

Use a calculator to investigate the effects of a and b on the graph of \(y=a b^{x}\) In the same viewing rectangle, graph \(y=2^{x}, y=4^{x},\) and \(y=8^{x} .\) How does an increase in the value of \(b\) affect the graph of \(y=a b^{x}\) when \(b>1 ?\)

Solve the equation. (Lesson 3.5) $$\frac{1}{4}(12 y-4)-2 y=-3(y-5)$$

Simplify the expression. Use only positive exponents. $$ \frac{36 a^{8} b^{2}}{a b} \cdot \frac{a b^{2}}{6} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \frac{3.5 \times 10^{-4}}{5 \times 10^{-1}} $$

Copy and complete the statement using \(<\) or \(>\). \((6 \cdot 3)^{3} ? 6 \cdot 3 \cdot 3\)

Rewrite the expression with positive exponents. $$ 3 x^{-4} $$

Use a calculator to investigate the effects of a and b on the graph of \(y=a b^{x}\) In the same viewing rectangle, graph \(y=\left(\frac{1}{2}\right)^{x}, y=\left(\frac{1}{4}\right)^{x},\) and \(y=\left(\frac{1}{8}\right)^{x}\) How does a decrease in the value of \(b\) affect the graph of \(y=a b^{x}\) when \(0

You buy 6 bagels and 8 donuts for a total of \(8.60. Then you decide to buy 3 extra bagels and 3 extra donuts for a total of \)3.75. How much did each bagel and donut cost? (Lesson 7.4)

Simplify the expression. Use only positive exponents. $$ \left(\frac{2 m^{3} n^{4}}{3 m n}\right)^{3} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \frac{6.6 \times 10^{-1}}{1.1 \times 10^{-1}} $$

Simplify the expression. \((3 b)^{3} \cdot b\)

If \(a^{0}=1(a \neq 0),\) 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.

Rewrite the expression with positive exponents. $$ x^{-2} y^{4} $$

Choose a positive value for \(b\) and graph \(y=b^{x}\) and \(y=\left(\frac{1}{b}\right)^{x} .\) What do you notice about the graphs?

Write the expression as a single power of the base. (Lesson 8.1) $$2^{2} \cdot 2^{2}$$

Simplify the expression. Use only positive exponents. $$ \frac{6 x^{2} y^{2}}{x y^{3}} \cdot \frac{\left(4 x^{2} y\right)^{2}}{x y^{2}} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \left(3 \times 10^{2}\right)^{3} $$

Simplify the expression. \(-4 x \cdot\left(x^{3}\right)^{2}\)

Rewrite the expression with positive exponents. $$ 8 x^{-1} y^{-6} $$

A store is having a sale on sweaters. On the first day the price of the sweaters is reduced by 20%. The price will be reduced another 20% each day until the sweaters are sold. On the fifth day of the sale will the sweaters be free? Explain.

Write the expression as a single power of the base. (Lesson 8.1) $$7^{6} \cdot 7^{2}$$

Simplify the expression. Use only positive exponents. $$ \frac{16 x^{5} y^{8}}{x^{7} y^{4}} \cdot\left(\frac{x^{3} y^{2}}{8 x y}\right)^{4} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \left(2 \times 10^{-3}\right)^{4} $$

Simplify the expression. \(\left(5 a^{4}\right)^{2}\)

Rewrite the expression with positive exponents. $$ \frac{1}{x^{-2}} $$

In 1995 you purchase a parcel of land for \(8000. The value of the land depreciates by 4% every year. What will the approximate value of the land be in 2002? $$(A) 224 \quad dollar$$ $$(B) 5760 \quad dollar$$ $$(C) 6012 \quad dollar$$ $$(D) 7999\) \quad dollar$$

Write the expression as a single power of the base. (Lesson 8.1) $$3^{5} \cdot 3^{2}$$

Simplify the expression. Use only positive exponents. $$ \frac{x^{2}}{x y^{-4}} \cdot \frac{2 x^{-3} y^{4}}{3 x y^{-1}} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ (0.5 \times 10)^{-2} $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$8 x+9=12$$

Simplify the expression. \(\left(r^{2} s^{3}\right)^{4}\)

Rewrite the expression with positive exponents. $$ \frac{2}{x^{-5}} $$

Simplify the expression. Use only positive exponents. $$ \frac{5 x^{-3} y^{2}}{x^{5} y^{-1}} \cdot \frac{\left(2 x y^{3}\right)^{-2}}{x y} $$