# Lesson 17

Annually, Quarterly, or Monthly?

- Let’s use different time intervals to solve problems.

### 17.1: Finding Equal Expressions

- Find pairs of expressions that are equal. Be prepared to explain how you know.
\((3^5)^2\)

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

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

\(3^6\)

\((3^2)^4\)

\(3^7\)

\(3^{10}\)

\(3 \boldcdot 9 \boldcdot 27\)

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

### 17.2: How Many Times Per Year?

- 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 - A gym membership has an annual fee, billed monthly. How much is each bill, if the annual fee in dollars is . . .?
- 360
- 540
- \(g\)

- An educational foundation gives an annual scholarship, distributed semi-annually. How much is each distribution, if the annual scholarship amount in dollars is . . .?
- 1,800
- 5,000
- \(s\)

- A magazine subscription has an annual price, billed quarterly. How much is each bill, if the annual price in dollars is . . .?
- 48
- 80
- \(m\)

### 17.3: Your Problems Are Compounded

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.