Answer:
e) none
Step-by-step explanation:
The first thing that we need to realise is that this question is set to a practical example of a ball being tossed into the air for a period of time. Thus, we know that:
a) time cannot be negative
b) a ball cannot travel a negative distance in height from where it was tossed it into the air (given that this starting position is also the ground)
In the context of what the problem asks us to achieve, which is to find the domain, we now know that:
a) t ≥ 0
b) the function h(t) is only practical when h(t) ≥ 0
In other words, we know that the domain starts at t = 0, however we need to find when the ball drops back onto the ground. We can do this by solving h(t) = 0:
h(t) = -16t^(2) + 96t
0 = -16t^(2) + 96t
0 = -16t(t - 6) (Factorise -16t^(2) + 96t)
So, now we get:
-16t = 0, therefor t = 0
or
t - 6 = 0, therefor t = 6
Thus, the ball is on the ground at t = 0 seconds and t = 6 seconds; it is between these two values of t that the domain exists and that the problem is practical.
Now, looking at the multiple choice options, it seems as though none of them are correct, therefor the answer would be e) none.
The other way to work through this question (particularly if it is just multiple choice) is that, after realising that the ball is tossed into the air at t = 0 seconds and then drops at some point later, we could already discount a), b) and c) as answers since they include infinity in the domain, which is not practical for this problem.
Then, we could substitute t = 5 into the equation to get:
h(t) = -16(5)^2 + 96*5
h(t) = -16*5*5 + 96*5
h(t) = -80*5 + 96*5
Since we need h(t) to be 0 at the end value of the domain, this is not the correct answer. Thus, the answer is e) none.
