Question

a function p estimates that there were 2,000 animals in a population in 1998. each year from 1998 to 2010, the function estimates that the number of animals in this population increased by 3% of the number of animals in the population the previous year. which equation defines this function, where p(x) is the estimated number of animals in the population x years after 1998? a ( p(x) = 2,000(3)^x ) b ( p(x) = 2,000(1.97)^x ) c ( p(x) = 2,000(1.03)^x ) d ( p(x) = 2,000(0.97)^x )

Explanation:

Step1: Recall exponential growth formula

The general form of exponential growth is $p(x) = P_0(1+r)^x$, where $P_0$ is the initial population, $r$ is the annual growth rate, and $x$ is time in years.

Step2: Identify given values

Initial population $P_0 = 2000$, growth rate $r = 3\% = 0.03$.

Step3: Substitute values into formula

Substitute $P_0$ and $r$ into the formula: $p(x) = 2000(1+0.03)^x = 2000(1.03)^x$.

Answer:

C. $p(x) = 2,000(1.03)^x$