Form Follows Function 2.7

​Form Follows Function

• multiplying

  • squared, tripled

• has a common ratio

• usually has percents (exponential growth or decay)

• deals with time

Geometric

• adding

• subtracting

• has a common difference

Arithmetic

Arithmetic vs Geometric

Open Ended

What is the common difference for this sequence?

$$16,\ 25,\ 34,\ 43...$$

Multiple Choice

What is the common ratio for this sequence?

$$12,-6,3,-\frac{3}{2}...$$

• there is none

• multiply -2

• divide 2

• divide -1/2

Categorize

Options (6)

Flowers cost $9 per dozen. The costs for 2 dozen, 3 dozen, 4 dozen and so on….

The price of a stock increasing by $0.48 per day

A cashier earns $15 per hour. The earnings for 1 hour, 2 hours, 3 hours, and so on

The first three terms of a sequence are 1, -6, 36, …

A bank account pays 4% interest compounded annually.

The value of gold is increasing by 15% each year.

Organize these options into arithmetic or geometric

Arithmetic

Geometric

Multiple Choice

In his job as a cashier, Joe makes $500 each month plus $20 every time he convinces a customer to open a charge account at the store.

What kind of function would this be?

• linear and continuous

• discrete and continuous

• linear and discrete

• exponential and discrete

Multiple Select

Pick the equation of the line with a slope of -1 through the point (-2, 5)

• y=-x+3

• y=x+3

• y=5x-2

• y=-(x+2)+5

Multiple Choice

What type of function would apply for $$f\left(n\right)=-3\left(5^{n-1}\right)$$

• linear and exponential

• exponential and discrete

• not enough information

• exponential and continuous

Drag and Drop

Write the equation for this graph

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Placeholder

=​

Placeholder

​

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

y

x

-3

3

+3

Open Ended

The population of the resort town of Java Hot Springs in 2013 was estimated to be 35,000 people, with an annual rate of increase of about 2.4%.

What word in this problem lets you know this is about exponential growth?

Open Ended

What do you know from the equation that would help you to graph the function?

$$y=\frac{1}{2}x-5$$