Question

A warren of rabbits has a population of 350. The population is increasing at a rate of 3% per year. How can you write an exponential growth function to find the monthly growth rate? (I have other question pls help if you can)

Answer 1

Answer:

$P(t) = 350e^{0.0025t}$

Step-by-step explanation:

Exponential growth function:

The exponential growth function for a population, after t years, is given by:

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

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

A warren of rabbits has a population of 350. The population is increasing at a rate of 3% per year.

This means that $P(0) = 350, r = 0.03$

So

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

$P(t) = 350e^{0.03t}$

How can you write an exponential growth function to find the monthly growth rate?

Monthly growth rate means that the time is divided by 12(as one year has 12 months), so the equation will be:

$P(t) = 350e^{0.03\frac{t}{12}}$

$P(t) = 350e^{0.0025t}$