Applications Of First Order Differential Equations

Question 1

For radioactive decay, what is the formula for the mass left after time t?

Answer 1

m(t) = m_oe^kt
m(t) = mass left after time t
m_o = initial mass
k = constant of proportionality/relative decay rate
t = time

Question 2

What is the relative decay rate (k) formula that involves dm/dt?

Answer 2

k = –dm/dt • 1/m
m is the mass remaining.

Question 3

For population growth, what is the formula for population size after time t?

Answer 3

P(t) = P_oe^kt

Question 4

What is the formula for relative growth rate?

Answer 4

k = dP/dt × 1/P
Where P = population grown/size.