Question

A population of 2000 starfish has a yearly per capita population growth rate of 0.012. By next year, how do you expect population size to have changed?
Assume that the population grows exponentially according to the equation d N d t = r N

It will increase by 50 starfish
It will increase by 24 starfish
It will increase by 100 starfish
It will increase by 200 starfish

Answer 1

Answer:

It will increase by 24 starfish

Step-by-step explanation:

The population is modeled by the following differential equation:

$\frac{dN}{dt} = rN$

Which has the following solution:

$N(t) = N(0)e^{rt}$

In which N(0) is the initial population and r is the growth rate.

A population of 2000 starfish has a yearly per capita population growth rate of 0.012.

This means that $N(0) = 2000, r = 0.012$

By next year, how do you expect population size to have changed?

This is N(1).

$N(t) = N(0)e^{rt}$

$N(1) = 2000*e^{0.012}$

$N(1) = 2024$

2024 - 2000 = 24

So the correct answer is:

It will increase by 24 starfish