Chapter Eight

Question 1

what is the formula for arc length?

Answer 1

note: it is easier to derive the formula than to remember it. To derive, simply differentiate ds² = dx² + dy² with respect to x

Question 2

what is the formula for exponential growth?

Answer 2

y = ce^kt

c is the initial amount of y at time t=0

k is the growth rate

t is the time

or

P = P₀e^kt

Question 3

what is the formula for logistic growth?

Answer 3

y = A ÷ (1 + ce^-Akt)

A is a fixed constant (such as the carrying capacity)

k is the growth rate

t is time

or

y = (AMe^kMt)/(1 + Ae^kMt)

Question 4

what is the formula for Euler’s Method?

Answer 4

y_n = y_n-1 + h * f’(x_n-1, y_n-1)

h is the step size

y’ = F(x_n, y_n)

or

y_n = (dy/dx)(∆x) + y

Question 5

what is the formula for approximate error?

Answer 5

exact value - approximate value = approximate error

Question 6

what is the formula for percent error?

Answer 6

(|exact value - approximate value| / |exact value|) x 100