Lesson 17

1. Find pairs of expressions that are equal. Be prepared to explain how you know.

   \((3^5)^2\)

   \((3 \boldcdot 3 \boldcdot 3 \boldcdot 3 \boldcdot 3) \boldcdot (3 \boldcdot 3)\)

   \(3 \boldcdot 3 \boldcdot 9 \boldcdot 9 \boldcdot 9\)

   \(3^6\)

   \((3^2)^4\)

   \(3^7\)

   \(3^{10}\)

   \(3 \boldcdot 9 \boldcdot 27\)

2. Write an expression that is equal to \((2^{30})^7\) using a single exponent.
3. Without evaluating the expressions, explain why \(2^{15}\) is equal to \(8^5\).

1. Complete the table.

   If something happens...	It happens this many times a year...	It happens every \(\underline{\hspace{.5in}}\) months...
   annually
   semi-annually
   quarterly
   monthly

2. A gym membership has an annual fee, billed monthly. How much is each bill, if the annual fee in dollars is . . .?
   1. 360
   2. 540
   3. \(g\)
3. An educational foundation gives an annual scholarship, distributed semi-annually. How much is each distribution, if the annual scholarship amount in dollars is . . .?
   1. 1,800
   2. 5,000
   3. \(s\)
4. A magazine subscription has an annual price, billed quarterly. How much is each bill, if the annual price in dollars is . . .?
   1. 48
   2. 80
   3. \(m\)

Match each item in the first column to a representation in the second column. 

1. A worker sets aside \$6,000 per year for their retirement fund by saving the same amount monthly.

A. \(6,\!000 \boldcdot 1.21^3\)

2. A business’s revenue increases by 20% per quarter. This happens for 2 years. Initially, their quarterly profit was \$6,000.

B. 

\(x\)	0	1	2	3	4	5
\(y\)	6,000	7,200	8,640	10,368	12,442	14,930

3. \(6,\!000 \boldcdot ((1.05)^{4})^x\)

C. \(6\boldcdot(3^4)^2\)

4. A man borrows \$6,000 from his sister. He will reduce the amount he owes in 1 year by paying her back quarterly.

D. 

\(x\)	0	1	2	3	4	5
\(y\)	6,000	4,800	3,840	3,072	2,457.6	1,966.1

5. A business’s revenue decreases by 20% semi-annually. This happens for 3 years. Initially, their quarterly revenue was \$6,000. 

E. \(6,\!000 \boldcdot 1.2155^x\)

6. The number of subscribers to a website triples quarterly for 2 years. Initially there were 6 subscribers.

F. \(6 \boldcdot 4,\!096^2\)

7. \(6,\!000 \boldcdot ((1.1)^2)^3\)

G.

8. The number of likes on a post was 6, and then for the next 2 years, the number of likes doubled, monthly.

H.