Word Problems
Linear vs Exponential
Interpreting Equations and Exponent Rules
Units 1-6 Spiral
Unit 7 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
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
100
Bear Mountain Summer Camp had 650 campers for its initial summer. After doing some advertising in the first off-season, the camp has enrolled 676 campers, and enrollment is expected to continue increasing each year at the same percent rate. Write an equation that can model the number of campers (y) after x years after the camp opened.
y=650(1.04)^x
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
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
Given the continuous exponential function below, identify the asymptote, domain and range.
Asymptote: y=3
Domain: All Real Numbers
Range: y>3
200
Which equation matches the graph below?
((BONUS!! Find the domain!))
a) y=3/5x+80 b) y=-5/3x+80
c) y=-3/5x+80 d) y=5/3x+80
C,
all whole numbers where
0<=x<=133
200
A $300 investment which compounds quarterly can be tracked using the equation below.
What is the percent interest earned each year?
4.2%
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
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
300
Given the below exponential function, what is the percent rate of decrease?
y=750(0.642)^x
35.8%
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
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. a) What would be the domain of the flight the airplane took? b) What would be the range?
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
a) all real numbers 0<=x<=4
b) all real numbers 0<=y<=9
400
Heather just got hired as an administrative assistant at Haven Enterprises. Her starting salary is $45,500, and her contract ensures that she will get a 3% salary increase each year. How much will her salary be after she's worked for Haven Enterprises for 25 years?
$95,266.90
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?
Between 5,159 and 5,173 cats!
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
500
Kristi takes out a business loan for $15,000 for a start up in home bakery. The interest rate is 12.5% which compounds quarterly.
a) Create an equation to model the compound interest situation above. b) If no loan payments are made, how much will be owed after 5 years?
a) A(t)=15000 (1+ 0.125/(4))^(4t)
b) $27,756.87