0

If we have a value e.g.

$$ B = 20000 $$

and it decreases at a constant instantaneous rate of say $$ -1.1*10^{-2} $$

per unit time.

What would B look like over say 300 time units, and how do we calculate this decline?

Thomas Andrews
  • 177,126
user1320502
  • 127

1 Answers1

0

Let B be the function decreasing in time. It is given that

$dB/dt=-1.1*10^{-2}$

Solving this equation gives

$B=-1.1*10^{-2} t+c $ where c is a constant

At t=0 we have B=2000 substituting this in the above equation gives c=2000.

Now substitute t=300 in the equation you will get B = 1996.7

Jasser
  • 1,976
  • Given the tag of exponentiation, I wonder if the intent was $dB/dt = -1.1\cdot 10^{-2} \cdot B(t)$. But hard to tell that from the question. – Thomas Andrews Sep 29 '14 at 14:22
  • Yes @Thomas Andrews the title seems to ask about exponential decay but as he describes in the post to be decreasing at a co Stanton rate – Jasser Sep 29 '14 at 14:30
  • @ThomasAndrews i have this somment in a paper "decreases at a constant instantaneous rate of -1.1 x10^-2" which i assumed to mean a linear straight line decline. But graphs in the paper show what looks like and exponential decline. So i was hoping just from the language of the sentence someone with better knowledge of nomencalture could explain what they mean – user1320502 Sep 29 '14 at 14:39
  • @user291957 i.e. the % of B left over time looks like an exponential decay, does thins mean it should be c*t^(−1.1*10^−2) – user1320502 Sep 29 '14 at 14:41
  • 1
    Are there no units in the paper? @user1320502 – Thomas Andrews Sep 29 '14 at 14:47
  • 1
    Assuming Thomas Andrews is right in his understanding and the title corresponds the equation he has written than the solution of the function is $B(t)=2000e^{-1.1*10^{-2} t}$ – Jasser Sep 29 '14 at 15:00