1. AB Unit 6B

2. 49. Steps for Euler’s Method
Approximation is based on tangent line
ynext = yold + dy/dx(△x)
Identify the step size, derivative, and initial value
Step size can be negative

3. Example Problem
Given dy/dx = x + 2 and y is 3 when x is 0. Use Euler’s method with step size 1/2
Find the value of y when x is 1.

4. 50. Relationship Between Direct Variation and Exponential Decay
If problems states rate of change is proportional to amount.
dy/dx = ky
If problems states rate of change is inversely proportional to amount
dy/dx = k/y

5. Example Problem
The rate of change of y is proportional to y. When t = 0, y = 2. When t = 2, y = 4. What is y when t = 3?

6. 51. Logistic Growth
This Logistic growth equation is presented ｙ＝M/(1+〖be〗^(-Mkt) ) ,dy/dt=ky(M-y) or dy/dt=ky(1-y/M)
Limit T approaches ∞, f(t) goes M.
Horizontal asymptote occur y=M
Point of maximum growth occur when y value get M/2

7. Example problem
The number N(t)N(t)N, left parenthesis, t, right parenthesis of people who have adopted a certain fashion style after ttt months satisfies the logistic differential equation: dN/dt=N(0.1-N/700000)
Initially, there were 3000 people who had adopted the style.
What is the number of people who have adopted the style when it's growing the fastest?
Solution
Find dN/dt=0
Take average for N
The answer is 35000

8. Play Quizizz!

9. Free Response

10. Answers