Introduction to Exponential Functions Growth/Decay Transformation Geometric Sequence

M&M Investigation Lap Handout Lab direction Materials Need: M&M’s Cup Napkin Lab Instruction/Question Worksheet

Investigation Discussion: What did you notice about your scatter plot? Is it possible to have zero value? Is it possible for these situation to be Linear? Quadratic?

Graph: 𝑦= 5 𝑥

Graph: 𝑦= 1 2 𝑥

What do you know? The two functions I just graphed are ___________________ functions. Exponential functions are equations in the form of ______________ where ________ and ________ are greater than zero. When the value of b is greater than 1, the graph of the function will ________________ from left to right. This is also known as exponential ______________. When the value of b is greater than zero but less than 1, the graph of the function will ______________ from left to right. This is also known as exponential _____________. The value of a is always the _______________ value or the _____________ amount. 𝑦=𝑎∙ 𝑏 𝑥 or 𝑦=𝑎 𝑏 𝑥

Circle the initial amount and put a box around the growth/decay factor Circle the initial amount and put a box around the growth/decay factor. Then determine if the problem represents growth or decay and if the graph will be increasing or decreasing. 1) y=3∙ 1.3 x 2) y=5000∙ 0.93 x 3) y= 1.065 x 4) y=10∙ 1 2 x 5) y=120000∙ 0.85 x 6) y= 1.234 x

Growth Keywords: Increase Up Appreciate

Decay Keywords: Decrease Going Down Depreciate

To Determine the Rate or “b” (when it isn’t provided for you): Change Percent to a Decimal Growth: 1 + decimal Decay: 1 – decimal Put this value into the equation for “b” Ex: increase by 12% Ex: decrease by 9%

Rewrite the following statements into the b-value that would be used in the equation. 1) increase by 3.5% 2) decrease by 6% 3) increase by 0.25% 4) decrease by 4.75%

Given the equation y = 35(0.57)x a) Does this equation represent growth or decay? _______________ b) What is the rate of growth or decay? _______________ c) What is the initial value? _______________ d) Evaluate for x = 5 _______________

Given the equation y = 225(1.23)x a) Does this equation represent growth or decay? _______________ b) What is the rate of growth or decay? _______________ c) What is the initial value? _______________ d) Evaluate for x = 2 _______________

Given the equation y = 154(1.06)x a) Does this equation represent growth or decay? _______________ b) What is the rate of growth or decay? _______________ c) What is the initial value? _______________ d) Evaluate for x = 7 _______________

Example 1: Raymond invested $4,000 in a new company. The value of his investment has been growing at a rate of 6% per year for the last 5 years. The function 𝐴=4,000 1.06 𝑡 represents the growth of his investment of $4,000, where A is the total value of his investment and t is the time invested in years. What is the total value of his investment after 5 years? Circle one: Growth or Decay Rate: Initial Amount:

Example 2: The value of a new car decreases as soon as it is driven off the dealer’s lot. The function 𝑉=30,000 .82 𝑡 models the depreciation of the value of a new car that originally cost $30,000, at a yearly decrease of 18%, where V is the value of the car and t is the time in years from the time the car was purchased. What is the value of the car after 3 years? Circle one: Growth or Decay Rate: Initial Amount: