Exponential Growth & Decay Flashcards

All 5 cards in this deck

What is exponential growth?

A quantity multiplied by the same factor greater than 1 in each time period.

What is exponential decay?

A quantity multiplied by the same factor between 0 and 1 in each time period.

What multiplier do you use for a repeated increase of $r\%$ per time period?

e.g. a population growing 6% per year

$1 + \dfrac{r}{100}$

For 6% per year the multiplier is $1.06$.

How do you find a population after several years of growth at a fixed percentage per year?

e.g. 25 000 workers growing at 6% per year, after 3 years

Multiply the starting number by the growth multiplier once for each year.

$25\,000 \times 1.06^3 = 29\,775$ workers

True or false? A population that decays by 20% each year will have reached zero after 5 years.

False. Each year it falls to 80% of the previous year's value, so it keeps getting smaller without reaching zero.