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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.

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Answer:

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Step-by-step explanation:

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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

[tex]n_{t} = n_{0}(r)^{t/k}[/tex]

where

[tex]n_{t}[/tex] is the population after t days

[tex]n_{0}[/tex] is the population at start (10)

[tex]r[/tex] is the rate at which population changes ie 3

[tex]t[/tex] is the number days from start

[tex]k[/tex] 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:

[tex]\\\\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[/tex]