Exponential Models
This is the f(x) that models a tree-planting drive starting with 2 members who each recruit 2 other each week.
What is
f(x) = 2^x
For
f(x) = 2^x
, this is the value of f(6).
What is 64
To solve for x in
2^x =8
, x equals this number.
What is 3
The students in Joy's Spanish class are planning a trip to Guatemala, during which they will stay with local host families. The number of host families they will need depends on the number of students who go on the trip.
f = the number of host families they will need
s = the number of students who go on the trip
Which of the variable is independent.
What is the number of students who go on the trip?
Because of its high potassium levels containing the isotope Potassium-40, this popular yellow fruit is naturally, harmlessly radioactive.
What is a banana?
This is the f(x) that models the peer tutoring network, in which each new member recruits 4 others each week.
What is
f(x)= 4^x
For
f(x) = 2*10^x
, this is the value of f(6).
What is 2,000,000?
Solve for x in
4^x = 16
.
What is 2
At a fancy dinner party, the number of courses that will be served determines how many forks will be set out by the hostess.
c = the number of courses served during dinner
f = the number of forks set out by the hostess
Which is dependent?
What is the number of forks set out by the hostess.
To protect itself from being dissolved by its own acid, this human organ creates a completely new layer of lining every few days.
What is the stomach?
This is the function f(x) that models a recycling initiative where 10 original leaders each recruit 10 new volunteers every week.
What is
f(x)= 10^x
For
f(x) = 2^(x-1)
, this is the value of f(6).
What is 32
The solution for x in the equation
5^x=125
.
What is 3
In a charity walkathon, the total money raised changes based on the miles walked. The total money raised is this variable.
What is the dependent variable?
What is the dependent variable?
This high-frequency sound wave technology allows bats and dolphins to "see" in total darkness by bouncing sound off nearby objects.
What is echolocation (or sonar)?
A campus robotics club starts with 5 founding members, and each week every member recruits 3 new students. This function models the number of new recruits in week x.
What is
f(x)= 5*3^x
For
f(x) = 2^3x
, this is the value of f(6).
What is 2621144
Find x if (1/3)x=9(1/3)x=9 in terms of exponents.
What is -2
Derek is building birdhouses in shop class. The amount of wood he has on hand determines how many birdhouses he can build.
w = the amount of wood Derek has on hand
b = the number of birdhouses Derek can build
Which of the variable is dependent?
What is the amount of wood?
Though they look like stinging jellyfish, comb jellies use rows of cilia to refract light and produce biological light through this process.
What is bioluminescence?
A student association starts with 12 members. Every 2 weeks, the total number of new members quadruples. This function models the new members recruited in week x.
What is
f(x)= 12*4^x/2 or f(x)=12*2^x
For
f(x) = 2^(x/2 -2) + 10
, this is the value of f(6).
What is 12?
The value of x in
10^x=0.01
What is -2
A campus gym tracks the total calories burned by a student based on how many minutes they spend on the treadmill. In this scenario, the number of minutes spent exercising represents this variable.
What is the independent variable x?
Formed by adding the previous two numbers together, this famous number sequence dictates the spiral patterns found on pinecones, seashells, and sunflowers.
What is the Fibonacci sequence?