Sequences
What do we call a sequence that is ADDING each time?
Arithmetic
What is 94% as a decimal?
0.94
What is our function for compound interest?
P(t)=P(1+r)^t
What direction does the x axis go?
Left and right
What do we use when we're trying to UNDO an operation? Looking for a vocab word here.
INVERSE operations
What is the COMMON DIFFERENCE of the following sequence? Answer in terms of d=____
10, 15, 20, 25...
d=5
Remember: Common difference is "what am I adding each time?"
If you spend $250 and pay 10% in sales tax, how much will you pay total?
$275
You deposit $100 into a savings account with 5% compound interest. Write the function using t for time.
P(t)=100(1+0.05)^t
What is the point at the center of our coordinate plane?
(0,0)
Solve using inverse operations (I need to see it on your board!)
x+3 = 8
x = 5
What type of sequence is this?
2, 4, 8, 16, 32, 64...
Geometric
(Geometric sequences are multiplying by the same amount each time!)
Write the function for the following question, leaving t as just the letter:
You deposit $400 into a savings account with an 8% interest rate.
P(t)=400+(400)(0.08)t
OR
P(t)=400+32t
You deposit $100 into a savings account with 5% compound interest. How much money will you have after 10 years? Round to 2 decimal places.
$162.89
Plot the point (3, 5)
We should start from (0,0), go RIGHT 3, and UP 5.
Solve using inverse operations
3x = 12
x=4
What is the common difference in the following sequence? Answer in terms of d=______
9, 4, -1, -6...
d=-5
Remember, if our sequence is going DOWN we are adding a negative!
You deposit $400 into a savings account with 8% interest. How much money will be in the account in 5 years and then 10 years?
You should have 2 answers!
5 years: $560
10 years: $720
You are the mayor of a town that's had a major landslide hit. Your population of 1200 has decreased by 12% for 2 years. What is your current population?
Write the function and round to the nearest whole number!
P(t)=1200(1-0.12)^2
929.28 rounded is 930
Plot the point (0, -3)
We should start from 0, go RIGHT 0, and then go DOWN 3.
FREEBIE: I'm going to show you the flowchart model for this equation:
2x + 3 = 11
Freebie!
What type of sequence is it and what is its common difference/ratio?
9, 27, 81, 243
Geometric, r=3
You spend $25 at a restaurant and pay a total of $30 including tip. What percent did you tip?
20% Tip
You deposit $5500 into a savings account with a 13% interest rate compounded annually. How much money will you have if you let it sit for 100 years?
Write the function!
P(t)=5500(1+0.13)^100
$1,117,396,808
Plot the point (-5, -2)
We should start at (0,0) and go LEFT 5 and DOWN 2.
Solve the following equation:
3w - 4 = 11
w = 5