Explicit --> Recursive
Exponential Functions
(IF.7e)
(IF.7e)
Determine Equation from Context.
(BF1a)
(BF1a)
Sequences
Sentence Frames.. Describing Sequences
100
Consider the following f(n) = -5n+6.
What is the recursive equation for the following explicit equation
*write next term as n+1
f(1) = 1
f(n+1) = f(n) -5
100
Which function has the most rapid rate of change?
a) 4(3x)
b) 6(4x)
c) 4(5x)
d) 5(2x)
c) 4(5x)
100
Tasha collects stamps. The total number of stamps in her collection, t, after m months is given by the equation t=3m+22.
Which sentence correctly describes the situation?
a) Tasha began her collection with 22 stamps and adds 3 each month
b) Tasha began her collection with 22 stamps and adds 22 each month
c) Tasha began her collection with 3 stamps and adds 3 each month
d) Tasha began her collection with 3 stamps and adds 22 each month
a) Tasha began her collection with 22 stamps and adds 3 each month
100
Look at this sequence.
3, 6, 12, 24, ...
Which function generates the sequence?
Let the domain of
the function be integers greater than or equal to 1.
a) f(x) = 1.5x2
b) f(x) = 1.5(3)x
c) f(x) = 3x
d) f(x) = x3
b) f(x) = 1.5(3)x
100
Describe the following Recursive Equation
A(1) = 4
A(n) = A(n-1) + 3
The first term is 4 and to find the next term we add 3 to the previous term.
200
Consider the following f(n) = -3n+7.
What is the recursive equation for the following explicit equation
*write next term as n+1
f(1) = 4
f(n+1) = f(n)-3
200
Which function represents exponential decay?
a)
b) f (x) = 44 + 0.44x
c) f (x) = 440 + 2.2x
d)
a)
200
The value of a certain stock has decreased 6% per day for the past 10 days. The initial price of the stock was $30 per share. Which equation describes the value of the share price of the stock as a function of n, the number of days elapsed during the 10 day period?
a)
b)
c)
d)
a)
200
What is the recursive formula for the following arithmetic sequence?
-5, -2, 1, 4, 7, ...
a) A(1) = 3
A(n) = A(n-1) -5 for n>1
b) A(1) = -5
A(n) = A(n) + 3 for n>1
c) A(1) = -5
A(n) = A(n-1) + 3 for n>1
d) A(1) = -5
A(n) = -5+3n for n>1
b)
A(1) = -5
A(n) = A(n-1)+3
200
Describe the following Recursive Equation
A(1) = 8
A(n) = A(n-1) -7
The first term is 8 and to find the next term we subtract 7 from the previous term.
300
Consider the following f(n) = 4n+3.
What is the recursive equation for the following explicit equation
*write next term as n+1
f(1) = 1
f(n+1) = f(n)+4
300
Which function represents exponential growth?
a)
b) f (x) = 44 + 0.44x
c) f (x) = 440 + 2.2x
d)
d)
300
A law firm charges $1,300 for an initial consultation, then $180 per hour of work. Which expression can be used to determine the cost of hiring the firm for h hours of work?
a) 180h-1300
b) 1300-180h
c) 1,300+ 180h
d) 1300+1300h+80
c) 1,300+ 180h
300
What is the recursive formula for the following geometric sequence?
9, 27, 81, 243, ...
a) f(1) = 9
f(n+1) = 3f(n), for all n>1
b) f(1) = 3
f(n+1) = 9f(n), for all n>1
c) f(1) = 9
f(n+1) = 3f(n+1) , for all n>1
d) f(1) = 9
f(n+1) = 9(3)n , for all n>1
a) f(1) = 9
f(n+1) = 3f(n), for all n>1
300
Write a recursive equation:
The first term is 1 and to find the next term we multiply the previous term by 9
A(1) = 1
A(n) = 9A(n-1)
400
Consider the following f(n) = 4(3)x.
What is the recursive equation for the following explicit equation
*write next term as n+1
f(1) = 12
f(n+1) = 3f(n)
400
The value of a house changes according to the function V(t) = 350,000 (1.05)t , where t is the time in years and V(t) is the value in dollars. Which statement best explains how the value is changing?
a) It is increasing by 1.05% per year
b) It is increasing by 5% per year
c) It is increasing by $1.03 per year
d) It is increasing by $350.00 per year
b) It is increasing by 5% per year
400
An ant population triples each month. If there are currently 600 ants, what will be the population in n months?
a)
b)
c)
d)
d)
400
The function below models the number of bonus points earned by for completing the nth level of a certain game.
f(n) = 3000-350n, where n = 1, 2, 3, 4, ...
Which sequence does f(n) generate?
a) 2650, 5650, 8650, 11650,...
b) 2650, 2300, 1950, 1600,...
c) 3000, 2650, 2300, 1950,...
d) 2650, 5300, 7950, 10,600,...
b) 2650, 2300, 1950, 1600,...
400
Write a recursive equation:
The first term is 10 and to find the next term we multiply the previous term by 2.
A(1) = 10
A(n) = 2A(n-1)
500
Consider the following f(n) = 2(5)x.
What is the recursive equation for the following explicit equation
*write next term as n+1
f(1) = 10
f(n+1) = 5f(n)
500
The value of a house changes according to the function V(t) = 230,000 (0.85)t , where t is the time in years and V(t) is the value in dollars. Which statement best explains how the value is changing?
a) It is decreasing by 85% per year
b) It is decreasing by 15% per year
c) It is decreasing by $0.85 per year
d) It is decreasing by $230.00 per year
b) It is decreasing by 15% per year
500
A college had 9,000 students enrolled in 2020, and the number of students enrolled has increased 3% every year. If f(n) represents the number of students enrolled after n years after 2020, then which function best represents its value?
a)
b)
c)
d)
b)
500
Consider the sequence shown,
6, 12, 18, 24, 30, ...
Assuming the domain for the function are positive integers greater than or equal to 1, which function represents this sequence?
a) f(x) = 6x+ 6
b) f(x) = 2x+6
c) f(x) = 6x+0
d) f(x) = 2x
c) f(x) = 6x+0
500
Describe the following sequence:
A(1) = 3
A(n) = 6A(n-1)
The first term is 3 and to find the next term we multiply the previous term by 6.