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

Answer:

Step-by-step 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:

$\\\\10.3^{3/3} = 10. 3^1 = 10.3 = 30\\10.3^{6/3} = 10. 3^2 = 10.9 = 90\\\\10.3^{9/3} = 10. 3^3 = 10.27 = 270$

Answer 2

Answer:

DO not working in you

Step-by-step explanation:

PLEASE help me in answering