Question

The population of a rabbit colony triples every 3 days. The population starts at 10 rabbits. Write an exponential function that will model the population of the colony after, t, days have passed.

Answer 1

DO not working in you

Explanation:

PLEASE help me in answering

Answer 2

Explanation:

The population at various days is as follows since population triples every 3 days

Day Population

0 10

3 30

6 90

9 270

.... ......

This can be modeled by the general equation

`n_(t) = n_(0)(r)^(t/k)`

where

`n_(t)` is the population after t days

`n_(0)` is the population at start (10)

`r` is the rate at which population changes ie 3

`t` is the number days from start

`k` is the number of days at which the population triples(here k =3 days)

We can check this by plugging in values for each of the variables

At day 0, population = 10(3)⁰ = 10. 1 = 10

Similarly populations for days 3, 6, 9 are:

`\\\\10.3^(3/3) = 10. 3^1 = 10.3 = 30\\10.3^(6/3) = 10. 3^2 = 10.9 = 90\\\\10.3^(9/3) = 10. 3^3 = 10.27 = 270`