Growth & Decay Quizzes, Questions & Answers

Top Trending Growth & Decay Quizzes

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 1
"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

Sample Question 2
The solution to dQ/dt = -0.08 Q is which of the following?

Q = Q(0) e^(-0.08t)

Q = Q(0) e^(0.08t)

Q = Q(0) / (1 - 0.08t)

Q = 100 e^(-0.08t)

Sample Question 3
A sample decays to 25% of its original amount in 14 days. What is the half-life?

7 days

10 days

14 days

28 days

Recent Growth & Decay Quizzes

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

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)

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

Questions: 15 | Attempts: 10 | 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)

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

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

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

Questions: 15 | Attempts: 11 | 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