Rate of growth of baster is proportional to the number of bacteria present at that time. If x is the number of bacteria present any instant t, then which one of the following is correct ?(take proportional constant equal to 1)

Options

A. x=log t
B. `x=ce^(t)`
C. `e^(x)=t`
D. `x=sqrtt`

Answer

B

Explanation

Rate of growth of bacteria `alpha` number of bacteria present at that time
` Rightarrow (dy)/(dx) alpha x Rightarrow (dx)/(dt) =x ` ( proportional constant =1)
` Rightarrow int 1/x dx =int dt`
` Rightarrow log x + log c`
` Rightarrow log x - log c =t`
` Rightarrow log (x/c) =t`
` Rightarrow x/c = e^(t)`
` x= ce^(t)`