Math 2 rules to remember

Power function

Exponential function

b has exponential growth when b > 1. But has exponential decay for 1<b<0

Graph power function

Has log on both sides

Exponential functions

Has log on only one side.

logarithmic scales

geometric sequence

Calculating t_n

a * r^n-1

How to calculate steady states for iteration processes

1. Make equation equal to t.

2. Then make that equation equal to zero

3. Find values for t

4. Then find first derivative of the original equation.

5. Put values for t in.

6. Steady: -1< f’(t) < 1, unsteady: f’(t) > 1 or f’(t) < -1

Growth rate

Derivative of f(x)

Relative growth rate

f’(x)/f(x)

Derivative an exponential function

f(x) = a^u

f’(x) = a^u * u’ multiplied by ln (a)

Integrating and exponential

a^x = a^x/ln(a)

cos and sin rule

Finding the average of a function (q4.21)

• Find integral

• Put in bounds

Integration by parts

Integration rule

steady states of differential equation (SO NOT ITERATION PROCESS)

Steady state y: f(y) = 0

Stable steady state y for f’(y) < 0

1. So first find the steady state by making the equation equal to zero and finding t

2. Then finding the stability by putting that number into the derivative equation.

3. If that number is smaller than zero it is stable!

integral of 1/cos(x)²

tan(x)

Formula doubling time

In this case, r=0.03

radioactivity formula

half life formula

where lambda is r value

exponential, bounded and logistic growth