Question

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Answer 1

Exponential Growth - Compound Interest
total = principal * (1+rate)^years
$1,000.00 deposited in a savings bank at 8% annual interest for 30 years will become $10,062.66 in 30 years.

Exponential Decay - Radioactive Decay
You have 100 grams of tritium (half life = 12.32 years). How much will remain after 30 years?
Ending Amount = Beginning Amount / 2^n
where n = elapsed time / half-life

Ending Amount = 100 / 2^(30/12.32)
Ending Amount = 100 / 2^2.4350649351
Ending Amount = 100 / 5.4078867332
Ending Amount = 18.49 grams

Answer 2

Exponential growth or decay is a rate of change that depends on the value of the function itself. In other words, y' = some function of y.

Real world examples:
EXP GROWTH: Growth of a plant (roughly), Population growth, Spread of a disease
EXP DECAY: Radioactive decay, Discharging capacitor