- [tex]P(t) = 20000 * 1.15^t[/tex]
- 80911
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Use an exponential growth function. The formula for exponential growth is:
- [tex]P(t)=P*(1+r)^t[/tex]
Where:
- P(t) is the future population
- P is the current or initial population
- r is the growth rate in decimals
- t is the time in years.
Given:
- P = 2000
- r = 15% = 0.15
- t = 10 years
Substitute the given values:
- [tex]P(t) = 20000 * (1 + 0.15)^t[/tex]
- [tex]P(t) = 20000 * 1.15^t[/tex]
To find the population in ten years (t = 10), we substitute:
- [tex]P(10) = 20000 * 1.15^{10}[/tex]
Calculating this:
- [tex]P(10) = 20000 * 1.15^{10} = 20000 * 4.04555773571 = 80911[/tex]
Therefore, the population in ten years will be approximately 80911.
