Growth and Decay

Question 1

L’Hospital’s Rule

Answer 1

If ƒ(c) = g(c) = 0 or ∞,

lim_x→c ƒ(x)/g(x) = ƒ’(c)/g‘(c)

Question 2

Euler’s Method

for solving differential equations

Answer 2

• Solve the differential equation for dy in terms of x, y, and dx.
• Substitute values of x, y, and dx to calculate a value of dy.
• Find the approximate new value of y by adding dy to the old value of y.
• Repeat the procedure to find the next value of dy at the next value of x.

Question 3

Logistic Differential Equation

Answer 3

dy/dx = ky•(M – y)/M

M = carrying capacity

Question 4

Logistic Function

Answer 4

y = M / ( 1 + ae^–kx )