Dissolving Sugar

Question

At 3pm on a particular day, 20kg of sugar is placed in a container of water and begins to dissolve. After t hours, the amount,x, of undissolved sugar is given by the formula x=20r^t. After 4 hours it is found that 10 kg of the sugar dissolved completely. At what time (to the nearest minute) will there be exactly 2kg of sugar remain undissolved? 

Answer 1

x = 20r^t

10 = 20r⁴

0.5 = r⁴

ln 0.5 = ln r⁴

ln 0.5 = 4 ln r

-0.6931 ≈ 4 ln r

-0.1733 ≈ ln r

0.84 ≈ r

 

2 = 20(0.84)^t

0.1 = 0.84^t

ln 0.1 = t ln 0.84

-2.30 ≈ -0.174t

13.23 ≈ t