Word Problems
Sequences
Linear vs Exponential
Interpreting Equations and Exponent Rules
Spiral
100
Jordan shakes hands with 8 people. The next day, each person shakes hands with eight more people. This continues for several days. Which function represents the number of people who will have shaken hands on the nth day?
y=8x
100
Given the two sequences below, find the 14th term of each.
f(n)=5(2)n-1
f(x)=12+4(x-1)
40,960 and 64
100
The table represents a ______ function because it increases by ________ over equal intervals of x.
The graph represents a _______ function because it decrease by ________ over equal intervals of x.
table: linear and equal differences
graph: exponential and equal factors
100
Given the function below, find the value of f(-6). Your answer should be an integer OR a fraction.
f(x)=15(3)^(x+1)
5/81
100
What would be the rate of change of the graph? INCLUDE UNITS IN YOUR ANSWER
____ balloons/minute ________ cm/minute
____ minute/cm ________ minutes/balloon
25 cm/minute
200
The amount of pollution in the lake can be modeled by the equation below. What is the best description of 1.16 in the function?
The amount of pollution will (increase/decrease) at a (constant rate/constant percent rate) of (16 pounds/16%).
y=200(1.16)^x
INCREASE, Constant PERCENT Rate, 16%
200
Given the sequence below, write the explicit formula.
1, 6, 11, 16 . . .
an=1+5(n-1)
200
Label each as linear or exponential:
1) Passengers depart off the train by 15% each stop.
2) The new highway is expanded 0.275 miles each day.
3) Your grade increases 15.85 points every 3 daily grades you complete.
4) The value of a new laptop loses one fifth of its value each year after being purchased.
Exponential, linear, linear, exponential
200
A $300 investment which compounds quarterly can be tracked using the equation below.
What is the percent interest earned each year?
4.2%
200
Which equation matches the graph below?
a) y=3/5x+80 b) y=-5/3x+80
c) y=-3/5x+80 d) y=5/3x+80
C
300
Maddy bought a rare Pokemon card worth $122. Since then, it has unfortunately been losing value by the same percentage each year. One year after Maddy bought the card, it was worth $95.75. Write an expression that can be used to predict the future value of the card. Round to the nearest hundredth when necessary.
y=122(0.78)x
300
Give the two formulas for the sequence:
15, 6, -3, -12...
an=15 - 9(n-1) and an=-9n+24
300
The first table is ______ because it changes at a ________ rate. The second table is ______ because it changes at a ________ rate.
First table: Linear, constant rate
Second table: Exponential, constant percent rate
300
What is the simplified form of the expression 9(9x)?
a) 18x b) 81x
c) 99x d) 9x+1
D
300
What is the average rate of change from 1.5 seconds to 2.5 seconds? Your answer MUST HAVE UNITS!
-64 feet / second
400
There are approximately 35,000 tons of recyclable waste in the county's dump. If the waste is being processed and reduced by 7% each year, what is the approximate of weight (in tons) left after 12 years? Round your answer to the nearest whole number.
14,651 tons
400
Consider the sequence:
90, 30, 10, 4/3, ...
What is the 10th term of the sequence?
10/2187
400
The red graph is ______ and it grows by _______.
The blue graph is ______ and it grows by _______.
The red graph is exponential and it grows by equal factors. The blue graph is linear and it grows by equal differences.
400
Given (3.2)8/x, which is equivalent?
a) ((3.2)^(1/8))^x
b) (3.2)^8*(3.2)^(1/x)
c) ((3.2)^8)^(1/x)
d)(3.2)^8+(3.2)^(1/x)
C
400
A paper airplane is launched from an 8 foot platform. What would be the domain of the flight the airplane took?
a) all real numbers -2<x<4 b) all integers -2<x<4
c) all real numbers x>0 d) all integers x>0
e) all real numbers 0<x<4 f) all integers 0<x<4
g) all real numbers x<8 h) all integers x<8
all real numbers 0<=x<=4
500
Three cats escaped the pound and formed a cat colony. After 1 year, there were 14 cats. After 2 years, that grew to 56 cats. 3 years in, there were 245 cats. 4 years later, there are 1241 cats. Based on this growth pattern, after 5 years, their population became an alarming how many cats?
5,173 cats!
500
Write the function to find any term of the sequence...
80, 60, 45, 33.75...
y=80(3/4)x-1
500
Given the function values below, justify whether the relationship is linear or exponential.
f(3)=16 and f(6)=22 and f(9)=28
Linear because... it increases at a constant rate.
Linear because... it changes by equal differences over equal intervals.
500
Select TWO expressions that are equal to 34x.
a) ((3)x)4 b) (3)x(3)4
c) (3)4(3)x d) ((3)4)x
e) (3)x+(3)4 f) ((3)1/4)x
A and D
500
What is the average rate of change from [-1, 4] on the function f(x)=3x2-4 ?
9