- A spherical mint of radius 5 mm is placed in the mouth and sucked. Four minutes later, the radius of the mint is 3 mm .
In a simple model, the rate of decrease of the radius of the mint is inversely proportional to the square of the radius.
Using this model and all the information given,
- find an equation linking the radius of the mint and the time.
(You should define the variables that you use.) - Hence find the total time taken for the mint to completely dissolve. Give your answer in minutes and seconds to the nearest second.
- Suggest a limitation of the model.