Answer:
Step-by-step explanation:
The population at various days is as follows since population triples every 3 days
<u>Day</u> <u>Population</u>
0 10
3 30
6 90
9 270
.... ......
This can be modeled by the general equation
![n_{t} = n_{0}(r)^{t/k}](https://tex.z-dn.net/?f=n_%7Bt%7D%20%3D%20n_%7B0%7D%28r%29%5E%7Bt%2Fk%7D)
where
is the population after t days
is the population at start (10)
is the rate at which population changes ie 3
is the number days from start
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](https://tex.z-dn.net/?f=%5C%5C%5C%5C10.3%5E%7B3%2F3%7D%20%3D%2010.%203%5E1%20%3D%2010.3%20%3D%2030%5C%5C10.3%5E%7B6%2F3%7D%20%3D%2010.%203%5E2%20%3D%2010.9%20%3D%2090%5C%5C%5C%5C10.3%5E%7B9%2F3%7D%20%3D%2010.%203%5E3%20%3D%2010.27%20%3D%20270)