# Geometric Sequence & Applications

Related Topics:
Common Core (Algebra)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn to choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A. Factor a quadratic expression to reveal the zeros of the function it defines.

B. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

C. Use the properties of exponents to transform expressions for exponential functions.For example the expression 1.15can be rewritten as (1.151/12)12t  ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%

### Suggested Learning Targets

• Use properties of exponents (such as power of a power, product of powers, power of a product, and rational exponents, etc.) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay.
Common Core: HSA-SSE.B.3c

Geometric Sequences Word Problems
Examples:
1. Bruno has 3 pizza stores and wants to dramatically expand his franchise nationwide. If the number of stores he owns doubles in number each month, what month will he launch 6,144 stores?
2. On January 1, Abby's troop sold three boxes of Girl Scout cookies online. Their daily goal is to sell double the number of boxes as the previous day. At this rate, how many boxes will they sell on day 7?
If this pattern continues, on what day will they sell 24,576 boxes of cookies? Compounding Interest and other Geometric Sequence Word Problems
Examples:
1. Suppose you invest \$1,000 in the bank. You leave the money in for 3 years, each year getting 5% interest per annum. How much money do you have in the bank after 3 years?
2. You invest \$5000 for 20 years at 2% p.a. How much will we end up with? How does this chnage is the interest is given quarterly? monthly?
3. If I can invest at 5% and I want \$50,000 in 10 years, how much should I invest now?
4. I decide to run a rabbit farm. I have 50 rabbits. The rabbit grows at 7% per week. How many will I have in 15 weeks?

Geometric sequence - salary
Example:
You land a job as a police officer. Your salary for the first year is \$43,125. You will receive 7% increase every year. How much will your salary be at the start of year six? Solve Word Problems using Geometric Sequences
Example:
Wilma bought a house for \$170,000. Each year, it increases 2% of its value.
a. Write the equation that represents the house's value over time.
b. What will the house be worth in 10 years? Application of a Geometric Sequence
Example:
Bouncing ball application of a geometric sequence
When a ball is dropped onto a flat floor, it bounces to 65% of the height from which it was dropped. If the ball is dropped from 80 cm, find the height of the fifth bounce. Population Growth and Compound Interest
This video gives examples of population growth and compound interest. Remember these examples are variations on geometric sequence.

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