In the beginning there are about 1000 bacteria in a testing tube and the amount of bacteria increases every two hours with 250 %. Use a recursion ecvation to tell the amount of bacteria after n days?
I made a formula for every two hours but i dont know how to countine after that.
y = (2,5x/2) + 1000
Where x is the amount of hours while y is the total amount of bacteria after x hours.
Edit: It should increase by 250% of what it was two hours ago, should be correct for those who noted my problems
The recursion formula is given by
$B_{n+1} = B_n+\frac{250}{100}B_n = \frac{350}{100}B_n$
We can rewrite this as;
$B_n = 3.5\cdot B_{n-1} =3.5(3.5\cdot B_{n-2})=3.5(3.5(3.5\cdot B_{n-3}))=\cdots=(3.5)^n\cdot B_0$
so as ; $B_0 = 1000$
$B_1 = 3.5\times 1000 = 3500$
$\vdots$
$B_n = (3.5)^n\cdot B_0$ where $n$ is the $n^{th}$ two hour mark.