when sugar is dissolved in waterthe amount A that remains af

when sugar is dissolved in water,the amount A that remains after t minutes satisfies the differential equation dA/dt = -kA (k>0). if 25 percent of the sugar dissolves after one minute, how long does it take for half the sugar to dissolve

Solution

Given

The amount of A dissolves water = t min

25percent dissolves = 1 min

25/100=1min

0.25 sugar disloves in 1min

Half of sugar disloves in water= ? Min

0.5sugar=?min

We know that 0.25+0.25= 0.5

Hence for half sugar to dissolve in water it takes = 2 min

O.25= 1

O.5= ?

0.25*t=0.5

t= 2min