The scale drawing can be used to approximate the area where a colony of 3,000 ants live. What is the population density of ants per square foot? Round to the nearest whole number.

We are given the two functions:

H(t) = −16 t^2 + 64 t + 12

g(t) = 10 + 10.4 t

Now let us calculate for values of H(t) and g(t) by plugging in the values of t = 1 to 4 in each function as shown in the table below:

t                              H(t)                        g(t)

1                              60                           20.4

2                              76                           30.8

3                              60                           41.2

4                              12                           51.6

Looking at the table, we can say that the time when H(t)=g(t) must be between t=3 and t= 4 seconds.

At t=3 seconds H(t) is above g(t), and at t = 4 seconds H(t) is below g(t). Therefore the two functions must be at the same height in between.

Part B. The solution in Part A gives us the exact time where the two objects have the same height. Further, we can see from the table that H(t) is decreasing meaning the projectile is going down while g(t) is increasing so the other projectile is going up.