calculating a decrease at constant instantaneous rate

Question

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?

Answer 1

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