5 Questions
In the context of growth and decay, what does the differential equation $\frac{dN}{dt} = kN$ represent?
Exponential growth
What is the original amount of bacteria in a culture if it is known to grow at a rate proportional to the amount present, and after 1 hour there are 1000 strands, and after 4 hours there are 3000 strands?
693.3641 strands
What is the half-life of a substance if its decay can be modeled by the equation $N(t) = N_0e^{-kt}$?
$\frac{0.693}{k}$
If a radioactive substance decays from 800 grams to 100 grams in 30 days, what is the decay constant $k$ in the equation $N(t) = N_0e^{-kt}$?
0.0316
What does a negative value of the constant of proportionality $k$ signify in the context of growth and decay?
Decay
Test your understanding of applications of differential equations with this quiz on growth and decay. Explore how to determine which applications to use and solve problems involving 1st order differential equations.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
