# P=f(t) gives the size of a population that begins with 19,000 members and grows at a continuous annual rate of 1.71%. Find a formula for the population.

$P=f\left(t\right)$ gives the size of a population that begins with 19,000 members and grows at a continuous annual rate of 1.71%.
Find a formula for the population.
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Quinn Hansen
Solution:
Initial population = 19000
Rate of grow =1.71% =0.0171
So, population after one year $=19000×\left(1+0.0171\right)$
population after two year $=19000×1.0171×1.0171\phantom{\rule{0ex}{0ex}}=19000×\left(1.0171{\right)}^{2}$
Similiarly
population after 't' years from beginning $=19000×\left(1.0171{\right)}^{t}$
$P=f\left(t\right)=19000\left(1.0171{\right)}^{t}$