Page 73 - Math Course 3 (Book 1)

Exponential Growth and Decay

MO. 2 - L6b Let’s Begin

Solve Problems Involving
Exponential Decay
Exponential Decay
Vocabulary A-Z

Let us learn some vocabulary Example

CHARITY

Exponential decay During an economic recession, a charitable
organization found that its donations dropped by
t
The equation for exponential decay is y = C(1 - r) 1.1% per year. Before the recession, its donations
where y is the final amount, C is the initial amount, were $390,000. Write an equation to represent
r is the rate of decay expressed as a decimal and t the charity’s donations since the beginning of the
is time. The initial amount decreases over time. recession.
t
y = C(1 - r) General equation for
Swimming exponential decay
A fully inflated raft loses 6.6% of its air every day.
t
The raft originally contains 4500 cubic inches of air. y = 390,000(1 – 0.011) C = 390,000 and r = 1.1%
or 0.011

y = C (1 – r) t General equation for y = 390,000(0.989) t Simplify.
exponential growth

= 4500(1 – 0.066) t C =4500 and r = 6.6%
or 0.066. Answer y = 390,000(0.989) t

= 4500(0.934) t Simplify.
CHARITY
An equation to represents the loss of air is During an economic recession, a charitable
t
y = 4500(0.934) , where y represents the amount of organization found that its donations dropped by
the air in the raft in cubic inches and t represents 1.1% per year. Before the recession, its donations
the numbers of days. were $390,000. Estimate the amount of the
donations 5 years after the start of the recession.
Key Concept y = 390,000(0.989) General equation for
t
exponential decay

General Equation for y = 390,000(0.989)5 t = 5
Exponential Decay
The general equation for exponential decay is y = 369,016.74
y = C(1 – r)t where y represents the final amount,
C represents the initial amount, r represents the The amount of donations should
rate of decay expressed as a decimal, and t Answer be about $369,017.
represents time.

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