GROWTH AND DECAYAPPRECIATION & DEPRECIATION

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WHAT YOU SHOULD LEARN

I can interpret coefficients and exponents in the context of the problem.

I can model and solve growth (appreciation) and decay (depreciation) problems.

EXPONENTIAL GROWTH

Like a bank account or credit card balance, other things can grow, decay, appreciate or depreciate exponentially.

Populations (bacteria) Value of Car Value of Real Estate

GROWTH AND DECAY FORMULA

A = P(1 + r)t

A = Final Amount P = Principal (initial amount) r = growth/decay rate (as a decimal)

If decaying/depreciating, be sure to make r a negative decimal

t = # of years/hours/minutes/etc.

EXAMPLE 1 Suppose that a small country has a

population of 10 million people and an annual growth rate of 4.5%

Write an equation to model the population.

How many people will there be in 25 years?

EXAMPLE 2

A Honda Accord cost $18,500 new in 2000. Suppose the car depreciated 8% per year.

Write an exponential equation to model its value?

How much will the car be worth in five years?

EXAMPLE 3 A Honda Accord cost $18,500 new in

2000. In 5 years it is worth $12,193. Find the rate at which the car is depreciating each year.

Write an exponential equation to model its value?

How much will the car be worth in 10 years?