Question

Kevin is observing the population of the fish he put into a pond. He built a pond and populated it with 500 fish. The population of the fish doubles every year.
Use x to represent the number of years and y to represent the population of the fish.

Answer 1

Here we will use exponential form, which is

$y = y_{0} e^{kt}$

Initial value, y0 = 500

Double of 500 = 1000

$1000 = 500e^{k*1}$

$2 = e^k$

$k= ln (2)$

Required equation is

$y=500e^{x ln2} \\ y= 500 (2)^x$