Exercise 3 Page 75

We first need to consider or find a quadratic function that models a real-life situation. Then, we use it to find the desired information. Suppose two rabbits are introduced to a deserted island. Let $P(t)$ be the number of rabbits after $t$ years. Suppose now we want to answer six questions.

1. How many rabbits are there when $t=0?$
2. After how many years does the population of rabbits reach its maximum?
3. How many rabbits are there when the population reaches its maximum?
4. After how many years will the rabbits will be gone?
5. State a reason for which the population may increase and then decrease.
6. Draw the graph of the function.

Let's work it out!

Question $1$

To find how many rabbits there are when $t=0,$ we need to substitute $0$ for $t$ in $P(t)=\text{-}4t^2+40t+2.$