Explicit & Recursive Sequences
What is a geometric sequence?
A sequence of numbers that have a "times" or "multiply" pattern
What is the formula for exponential growth/decay?
f(x)=ab^x
What is domain?
all x-values or all inputs
What is the formula for simple interest?
I = Prt
Is the following a function? Yes or no?
The assignment of students to locker numbers.
Yes, each student is assigned only one locker
What is an arithmetic sequence?
A sequence of numbers that have an "add" or "subtract" pattern
What are the characteristics of a linear graph?
They are a straight line
What is range?
All y-values or all outputs
FV=PV(1+r)^t
If g(x)=7x^2+1/2, what is g(-2)?
g(-2) = 29
List the first five terms of the following sequence: f(n) = 4n – 1, n ≥1
3, 7, 11, 15, 19
What are the characteristics of an exponential graph?
They are a curve
What is the domain of g(x) = 2x^2 + 10?
Domain = (-infinity, +infinity)
Cindy invests $325 at Access Federal Credit Union that pays 6% simple interest, how much money will Cindy have in her account after 3 years?
I = (325)(.06)(3) = $58.50 ... $325 + $58.50 = $383.50
If f(x) = 6x – 9 and g(x) = 0.5(2)^x, what is f(3)+f(4)?
f(3) = 9, f(4) = 15 ... 9 + 15 = 24
Write a recursive sequence for the following sequence: 2, 4, 8, 16, 32,...
f(n) = f(n-1) X 2 , a(1) = 2
Does the following formula show exponential growth or exponential decay? f(t)=2/3(3)^t
Since 3 > 1, exponential growth
The function f has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}. Could f be represented by {(1,2), (3, 4), (5, 6), (7,2)}? Yes or no?
Yes, domain = x-values and range = y-values.
Johnny deposits $12,300 into his savings account at City Bank. The bank pays 4% interest compounded annually. How much money will Johnny have after 10 years if he does not withdraw any money?
FV=12,300(1+.04)^10 = $18,207
If g(x) = -3x – 3 and h(x) = 8x/2+1, what is g(-7) - h(1)?
Write an explicit formula for the following sequence: 0, -3, -6, -9, -12,….
f(n) = -3n + 3
Given the equation of the exponential graph g(x) = 2(2^x), when the input(x-value) is 0 what is the output(y-value)?
y = 2
What is the domain AND the range of h(x) = 3^2x?
Domain = (-infinity, +infinity), Range = (0, +infinity)
James has $700 to invest at Country Bank that pays 9% compound annual interest. How many years will it take for her bank account to reach over $1,500?
9 years = $1,520.33
If f(x) = 6x – 9 and g(x) = 0.5(2)^x, what is g(6)/g(3)?
g(6) = 32, g(3) = 4 ... 32/4 = 8