Population Growth of Birds

In a certain city, the population growth of a particular species of bird is modeled by the function:

$$ P(t) = P_0 e^{rt} $$

where:

• $$ P(t) $$ = the population at time $$ t $$,
• $$ P_0 $$ = the initial population,
• $$ r $$ = the growth rate (as a decimal), and
• $$ t $$ = time in years.

A conservation organization starts with an initial population of 500 birds ($$ P_0 = 500 $$). They estimate that the birds' population grows at a rate of 3% per year ($$ r = 0.03 $$). Over time, they would like to know the population after 10 years. What will be the population of the birds after this period?