Sequences
What is the growth pattern for the sequence?
6, 11, 18, 27 ?
constant second difference of +2
An online game has 7453 users. The number of users is increasing at a rate of 3.5% per week. What is model should be used to represent this problem?
f(x) = 7453 (1+.035)^t
Growth or Decay?
y = 16(1.34)^x
growth
Parent f(x) = (1/2)x
g(x) = 5(1/2)x-3
The graph pf g(x) has been translated ____ to the _____
3 to the right
Linear functions always have ______rates of change.
constant
What is the growth pattern and the type of function in the following sequence?
3, 12, 48, 192....
times 4
exponential
The population of a community is decreasing at a rate of 8% per year. There were 600 people in the community 4 years ago. How many people are there now?
429 people
growth or decay?
y = 5(2/3)^x
decay
Parent f(x) = (1/2)x
g(x) = 5(1/2)x-3
g(x) has been _________________ vertically
stretched
Nonlinear functions always have _______rates of change.
variable
What is the growth pattern and the next three terms?
4, 12, 36, 76
constant second difference of 16
132, 204, 292
Steven buys stock for $1000. The stock gains value at a rate of 4.2% each year. What is the value of the stock in 12 years?
$1638.37
Growth or decay and percentage.
y = 14(.72)^x
Decay
28%
Parent: f(x) = (1/2)x
g(x) = (1/2)x + 1 - 4
The y-intercept of f(x) is ______
The y-intercept of g(x) is _______
f(x) (0,1)
g(x) (0,-3.5)
Determine the rate of change between each ordered pair in the table.
-2/2, -4/4, -2/2, -4/4
-1,-1,-1,-1
What is growth pattern, type of function and next 3 terms?
4, 9/2, 5, 11/2, 6 ...
+1/2
Linear
13/2, 7, 15/2
Iodine-131 has a half-life of 8 days. The original mass of the sample was lost. After 24 days, 3.75 grams remains. How many grams was the original sample?
30 grams
growth or decay and percentage
y = 7(1/5)x
Decay
80%
Parent: f(x) = (1/2)x
g(x) = (1/2)x + 1 - 4
The graph of g(x) has been translated 1 _____
and 4 units ______
1 left
4 down
Determine the rate of change between each ordered pair in the table.
-3.2, -1.2, .8, 2.8
The first term of a geometric sequence is 3 and the common ratio is 5. What is the 15th term?
1.83 x 10^10
or
18310546880
Gavin invests $4800 at a rate of 3.5% compounded semiannually. About how many years will it take for his investment to exceed $5500?
4 years
growth or decay and percentage
y = -14.5(6/5)x
Growth
20%
List three mathematical facts to compare the following functions.
f(x) = (1/2)x
g(x) = x2 - 4
f(x) is exponential; g(x) is quadratic
No reflection has happened to either
f(x) is not shifted up or sideways; g(x) shifted down
A table has rates of change of -3, 3, -3 and 3 between its sets of ordered pairs. What two things do these results tell us?
Variable rate of change
Nonlinear function