Growth & Decay Quizzes, Questions & Answers

Top Trending Growth & Decay Quizzes

Exponential Growth, Decay & Logistic Basics (k, half-life, carrying capacity)

Are you ready to see how real-life change can be modeled with one simple equation? In this quiz, you’ll explore differential equations where the rate of change depends on the current amount, like dy/dt = ky. You’ll...

Questions: 15 | Attempts: 16 | Last updated: Feb 3, 2026

Sample Question
A population grows at a rate proportional to its current size. Which differential equation models this situation?

Dy/dt = k(y - 100)

Dy/dt = ky

Dy/dt = k/y

Dy/dt = constant

Half-life, Newton’s Law of Cooling & Conceptual Logistic Growth (Equilibria & Max Growth)

Ready to model how things move toward a target value? In this quiz, you’ll explore equations where the rate depends on the difference between a quantity and a surrounding constant, like temperature moving toward room...

Questions: 15 | Attempts: 23 | Last updated: Feb 3, 2026

Sample Question
"The rate of change of a population is proportional to the current population" translates to which differential equation?

DP/dt = k

DP/dt = kP

DP/dt = k(P - M)

DP/dt = k/P

Differential Equation Models: Exponential, Logistic, Cooling & Data Interpretation

Can you spot the difference between unlimited growth and growth with limits? In this quiz, you’ll learn how logistic models describe populations that grow quickly at first but slow down as they approach a maximum...

Questions: 15 | Attempts: 11 | Last updated: Feb 3, 2026

Sample Question
A population of bacteria grows at a rate proportional to its current size. Which differential equation correctly models this situation?

Dy/dt = k(y - 1000)

Dy/dt = ky

Dy/dt = k/y

Dy/dt = k(1000 - y)

Recent Growth & Decay Quizzes

Real-World DE Modelling: Interest, Half-Life & Logistic Population Dynamics

Ready for deeper reasoning and bigger applications? This quiz takes logistic and exponential models further by focusing on how growth rates change over time and what happens near key points like half the carrying capacity....

Questions: 15 | Attempts: 10 | Last updated: Feb 3, 2026

Sample Question
The rate of spread of a rumor is proportional to the product of the number who know it and the number who don’t. If the town has 10,000 people, which differential equation models the number P(t) who have heard the rumor?

DP/dt = kP

DP/dt = kP(10000 - P)

DP/dt = -kP(10000 - P)

DP/dt = k(10000 - P)

Exponential Growth/Decay Applications & Intro to Logistic and Cooling Models

Think you can predict the future of a quantity just from its rate? This quiz challenges you to use half-life and doubling time ideas to solve exponential growth and decay problems. You’ll work through scenarios involving...

Questions: 15 | Attempts: 13 | Last updated: Feb 3, 2026

Sample Question
A quantity changes at a rate proportional to itself and is currently decreasing. What is the sign of k in dy/dt = ky?

K > 0

K = 0 ‘

K < 0

Cannot determine