9.4 Exponential Growth & Decay

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Presentation transcript:

9.4 Exponential Growth & Decay

The Law of Natural Growth: If Then

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

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

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

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

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

9.5 The Logistic Equation

The Logistic Model: K: carrying capacity

The Logistic Model: K: carrying capacity

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

HW: 9.5 pg. 619 # 1 & 3

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