7 As a spherical snowball melts its volume decreases. The rate of decrease of the volume of the snowball at any given time is modelled as being proportional to its volume at that time. Initially the volume of the snowball is \(500 \mathrm {~cm} ^ { 3 }\) and the rate of decrease of its volume is \(20 \mathrm {~cm} ^ { 3 }\) per hour.
- Find the time that this model would predict for the snowball's volume to decrease to \(250 \mathrm {~cm} ^ { 3 }\).
- Write down one assumption made when using this model.
- Comment on how realistic this model would be in the long term.