Atoy rocket is launched from a platform that is 48 ft high. the rocket height above the ground is modeled by h=-16t^2+32t+48. a) find the maximum height of the rocket b) find the time it will take for the rocket to reach the ground

a) 64 feet

b)  3 seconds

Step-by-step explanation:

a)

The maximum height of can be bound by finding the y-coordinate of the vertex of .

Compare this equation to to find the values of .

.

The x-coordinate of the vertex can be found by evaluating:

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating at :

So the maximum height of the rocket is 64 ft high.

b)

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

I'm going to divide both sides by -16:

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

This implies we have either or

The first equation can be solved by adding 3 on both sides: .

The second equation can be solved by subtracting 1 on both sides: .

So when seconds, is when the rocket has hit the ground.

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6