Q1.
What will be the height of the water at the end of 5 months?
Answer
The height after t months is h(t) = 3 − 0.5t.
h(5) = 3 − 0.5 × 5
= 3 − 2.5
= 0.5 m
= 3 − 2.5
= 0.5 m
Why this is decay and how far it can be trusted: the coefficient of t is −0.5, so the water level drops by a fixed half-metre every month regardless of how full the tank is. That constant drop is what makes h linear, and its negative sign is what makes it decay rather than growth. The model also tells us when the tank empties: 3 − 0.5t = 0 gives t = 6 months. Past that the formula would report a negative depth, so the model stops being physical there.
Check it yourself: extend the book’s table — 3, 2.5, 2, 1.5, 1, 0.5, 0 for t = 0 to 6. The differences are all −0.5, as a linear pattern demands.