General Sequences
Recursive or explicit?
an = -2n2 + 1
Explicit
30, 27, 24, 21, ...
f(n) = -3n + 33
You want to buy a new TV for $2100, but you have to save up over time. You save $25 in the first month, $35 the second month, $45 the third month and so on. How much will you have saved in the 12th month?
f(12) = $135
x - 0 3 6
y - 10 5 0
Linear decay
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?
f(3) = $17,120.42
Recursive or explicit?
f(1) = 2 and f(n) = 2f(n-1) - 6
Recursive
5, -1, 1/5, -1/25, ...
f(n) = 5(-1/5)n-1
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
x - 0 1 2 3
f(x) - 9 27 81 243
Exponential growth
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.
State whether the following sequences are arithmetic, geometric, or neither, then state the common difference or ratio if applicable.
6, 24, 96, 384, ...
Geometric
r = 4
-2, -6, -18, ...
f(n) = -2(3)n-1
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
The half-life of a certain element is 52 days. (Half of the material is gone every 52 days.)
Exponential decay
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.
State whether the following sequences are arithmetic, geometric, or neither, then state the common difference or ratio if applicable.
1, 2, 6, 24, ...
Neither
-5, 16, 37 ...
f(n) = 21n - 26
Arithmetic sequences are modeled by __________ functions.
Linear
f(x) = 4(2)x-3 - 7
Exponential growth
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.
After how many months will Flu A infect more people than Flu B?
After 31 months
State whether the following sequences are arithmetic, geometric, or neither, then state the common difference or ratio if applicable.
5/2, 11/6, 7/6, 1/2, -1/6, ...
Arithmetic
d = -4/6
27, 13, -1, ...
f(n) = -14n + 41
Geometric sequences are modeled by ___________ functions.
Exponential
f(x) = 2(1/2)x+3
Exponential decay
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 two thousand dollars in 2010, how much could it be sold for in 2017?
$2,721.72