1. 9.4 Exponential Growth & Decay

2. The Law of Natural Growth:If
Then

3. “Proportionality Constant”
k is the
“Proportionality Constant”
k>0 for growth
k<0 for decay

4. Direct Variation y varies directly as x.
y is directly proportional to x.
y is proportional to x.

5. Some Applications
Population Growth
Radioactive Decay
Unimolecular 1st order reactions
Value of account with continually compounded interest

6. Newton’s Law of Cooling:If
*T is temp of surroundings
Then

7. HW: 9.4 pg. 610 # 1, 3, 13, 20

8. 9.5 The Logistic Equation

9. The Logistic Model:
K: carrying capacity

10. The Logistic Model:
K: carrying capacity

11. Equilibrium Solution: the y-value where the solution equation “flattens out” or remains constant.

12. HW: 9.5 pg. 619 # 1 & 3

13. Inverse Variation y varies inversely as x.
y is inversely proportional to x.