The situations that describe an exponential growth are:
- The number of butterflies in an area increases by 10% per year.
- Kristy bought a collector’s coin for $2.15 and its value increases at a rate of 3% per year.
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The number of people who have heard a rumor increases because every person tells 2 other people.
Exponential growth is growth that increases with as the population grows.
Exponential growth can be represented with this equation: [tex]f(x) = a( 1 + r)^{x}[/tex]
Where:
a = initial value
r = growth rate
x = year
The growth rate of the butterflies increase by 10% every year. Assume that the current population of butterflies is 10. In 10 years, the population of the butterflies would be:
100 x (1.1)^10 = 2593.7
The growth rate of butterflies can be modelled as an exponential growth.
The population of the city increases at a constant rate each year. Thus, it cannot be modelled as an exponential growth.
The increase in the value of Kristy's collector's coin can be modelled using an exponential growth equation.
$2.15 x [tex](1.03)^{x}[/tex]
Where x represents years.
The growth rate of people who hear the rumour is exponential. When2 people hear the rumor, they would tell 4 people (2 x 2). The 4 people would tell 8 people (4 x 2) .
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