When sugar is dissolved in water, the amount a that re- mains undissolved after t minutes satisfies the differential equation da=dt d! ka (k> 0). if 25% of the sugar dis- solves after 1 min, how long does it take for half of the sugar to dissolve?

Sugar will dissolve to half of it's amount in 2.41 minutes.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

When the sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfies the differential equation

If 25% of the sugar dissolves after 1 min, how long does it take for half of the sugar to dissolve.

The given differential equation is

In other form, dA = -kA.dt

We further integrate the equation,

lnA = -kt + c

Or

A = -----(1)

Here is a constant.

For t = 0,

Let

Therefore, equation (1) will become

A =

If sugar dissolves 25% in 1 minutes then undissolved sugar will be

100 - 25 = 75%

Now from the equation

By taking natural log on both the sides

k = 0.2877

Now we have to calculate the time to dissolve half of the sugar, that means half the sugar will be undissolved.

Form the equation,

ln(0.5) =

0.6931 = 0.2877t

t = 2.41 minutes

i think it is 70

step-by-step explanation: