What’s a Function?
A function assigns each input to how many outputs?
Exactly one
Arithmetic sequences grow by a constant ___?
Difference
Geometric sequences grow by a constant ___?
Ratio
Saving $10 each week is what type of sequence?
Arithmetic (linear)
There are two types of flu spreading in Santa Clarita. Flu A is infecting the population at a growing rate of 16% each month with an initial population of 5 people. Flu B is infecting the population by an additional 15 people each month with an initial population of 5 people.
Which flu is linear and which flu is exponential?
Flu A is exponential, and Flu B is linear.
Is the relation {(1, 2), (2, 3), (1, 4)} a function? Why or why not?
No, because input 1 has two outputs
Arithmetic sequences are modeled by __________ functions.
Linear
Geometric sequences are modeled by ___________ functions.
Exponential
A cell population doubles every day. What type of sequence?
Geometric (exponential)
There are two types of flu spreading in Santa Clarita. Flu A is infecting the population at a growing rate of 16% each month with an initial population of 5 people. Flu B is infecting the population by an additional 15 people each month with an initial population of 5 people.
How many people will be infected by each of the flu types after 20 months?
Flu A infects 97 people after 20 months, and Flu B infects 305 people.
Is the relation {(1, 2), (2, 3), (6, 4), (9,4)} a function? Why or why not?
Yes, this relation is a function, because every input has exactly one output.
Write the first 4 terms if a1=3 and d=4
3, 7, 11, 15
Write the first 4 terms if a1 = 2, r = 3
2, 6, 18, 54
You put $500 in a savings account that earns 5% interest. Is this arithmetic or geometric?
Geometric (growth by multiplying)
You purchased a car in 2012 for $25,999. It is depreciating at a rate of 13% each year. How much will the car be worth in 2015? Round to the nearest cent.
f(3) = $17,120.42
Chase is planning a fundraiser where he sells custom t-shirts. Each t-shirt costs $12 to make, and he plans to buy the machine to make then which cost $50. Write a function that represents Chase’s total amount spent if he plans this fundraiser.
C(x)=12x+50
Explicit formula for 2, 6, 10, 14, …
an = 2 + 4(n−1)
Explicit formula for 5, 10, 20, 40, …
an = 5 x 2n-1
Which type of sequence will eventually grow faster: arithmetic or geometric? (d>1; r>1)
Geometric, because multiplying grows faster than adding
The cost of a particular piece of artwork is increasing exponentially, according to the formula C(t) = d(1.045)t where d represents the initial value of the art.
If the artwork was originally worth $2000 in 2010, how much could it be sold for in 2017? Round to the nearest cent.
$2,721.72
I want to get Skittles from the vending machine for $1.50, when I insert my money, it spits out m&m's, but I tried again cause I can't eat chocolate and it finally gave me skittles. Is this a function?
No, because one input gives two outputs
Edgar is getting better at math. On his first quiz he scored 57 points, then he scores 61 and 65 on his next two quizzes. If his scores continued to increase at the same rate, what will be his score on his 9th quiz?
f(9) = 89 points
In a certain region, the number of highway accidents increased by 8% each year, over a four-year period. How many accidents were there in 2006 if there were 5,120 accidents in 2002? Round to the nearest whole number.
f(5) = 6,966 accidents
A sequence doubles each time: 1, 2, 4, 8,....
If you graph the points (n,an), will the graph curve upward, form a straight line, or stay flat?
It will curve upward because it’s a geometric (exponential) sequence.
In a certain region, the number of highway accidents increased by 8% each year, over a four-year period. How many accidents were there in 2006 if there were 5,120 accidents in 2002? Round to the nearest whole number.
f(5) = 6,966 accidents