Arithmetic Sequences
Arithmetic sequences have a common __________.
Difference
Geometric sequences have a common __________.
Ratio
Evaluate the following function.
y = 4x
x = 7
y = 16,384
You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What exponential function will represent the value of the land?
y = 30000(1.05)x
a = 30000
b = 1 + 0.05 = 1.05
y = 3x+ 9
What is the type of function?
Name its x- and y- intercepts.
Linear Function
x-intercept: (-3,0)
y-intercept: (0,9)
What two operations are involved in arithmetic sequences?
Addition and Subtraction
What two operations are involved in geometric sequences?
Multiplication and Division
Evaluate the following function.
y = 3 * 5x
x = 3
y = 375
During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL.
y = 500 (0.88)x
a = 500
b = 1 - 0.12 = 0.88
y = x2 - 7
What is the type of function?
Name its domain and range.
Quadratic Function
Domain: (-∞ , ∞)
Range: [-7, ∞)
Is the following an arithmetic sequence:
1 , 7, 13, 19, 25...
If so, what is the common difference?
Yes, the common difference is 6.
Is the following a geometric sequence:
3, 9, 27, 108
If so, what is the common ratio?
No.
Evaluate the following function.
f(n) = 7n - 3
What is the first term?
a1 = 4
f(1) = 71 - 3
= 7 - 3
You deposit $1600 in a bank account. Find the balance after 3 years if the account pays 4% interest yearly.
1,799.78
a = 1600
b = 1 + 0.04 = 1.04
x = 3
y = 1600(1.04)3
y = 4x - 7
What is the type of function?
Name its end behavior.
Exponential Function
x → -∞ , y → -7
x → ∞ , y → ∞
Is the following an arithmetic sequence:
42, 35, 28, 21, 16
If so, what is the common difference?
No.
Is the following a geometric sequence:
416, 104, 26, 6.5, 1.625
If so, what is the common ratio?
Yes, the common ratio is 0.25.
What is the value of the output of the following function when the input value is 2.
f(x) = 6 * 2x - 1
f(2) = 12
f(2) = 6 * 22 - 1
= 6 * 21
= 6 * 2
Suppose $2,000 is deposited in an account paying 2.5% interest compounded semiannually. What will the account balance be after 12 years?
$2,694.70
A= 2000(1 + 0.025/2)2(12)
y = -7x + 5
What is the type of function?
Name its intervals of increase/decrease.
Linear Function
Increase: None
Decrease: (-∞ , ∞)
4, 13, 22, 31, 40
What is the 11th term?
94
a1 + (n - 1)d
4 + (n - 1)9
4 + (11 - 1)9
4 + (10)9
4 + 90
7, 14, 28, 56, 112
What is the 20th term?
3,670,016
a1 * rn-1
7 * 220-1
7 * 219
7 * 524288
In a hospital, a patient was administered 400 milligrams of saline. The function below can be used to determine the amount of saline in the patient's bloodstream after x hours.
f(x) = 400(1/2)x/2
How many milligrams of saline are present in the patient's blood after 6 hours?f(6) = 50
f(6) = 400(1/2)6/2
= 400(1/2)3
= 400(1/8)
Lisa invested $1,000 into an account that pays 6% interest compounded monthly. If this account is account is for her newborn boy, how much will the account be worth on his 21st birthday?
$3,514. 37
A = 1000(1 + 0.06/12)12(21)
y = x2 - 8x + 12
What is the type of function?
Name its intervals of increase/decrease.
Quadratic Function
Increase: (4, ∞)
Decrease: (-∞, 4)