Technology required. Two rocks are launched straight up into the air. The height of Rock A is given by function \(f\), where \(f(t) = 4 + 30t - 16t^2\). The height of Rock B is given by function \(g\), where \(g(t) = 5 +20t - 16t^2\). In both functions, \(t\) is time measured in seconds and height is measured in feet.

Use graphing technology to graph both equations. Determine which rock hits the ground first and explain how you know.

Each expression represents an object’s distance from the ground, in meters, as a function of time, \(t\), in seconds.

Object A: \(-5t^2+25t+50\)

Object B: \(-5t^2+50t+25\)

1. Which object was launched with the greatest vertical speed?
2. Which object was launched from the greatest height?

Here is a pattern of dots.

1. Complete the table.
2. How many dots will there be in Step 10?
3. How many dots will there be in Step \(n\)?

step	total number of dots
0
1
2
3

A function, \(f\), is defined by \(f(x)=2^x\), and a function, \(g\), is defined by \(g(x)=x^2+16\).

1. Find the values of \(f\) and \(g\) when \(x\) is 4, 5, and 6.
2. Are the values of \(f(x)\) always greater than the values of \(g(x)\), for all \(x\)? Explain how you know.

Han accidentally drops his water bottle from the balcony of his apartment building. The equation \(d=32-5t^2\) gives the distance from the ground, \(d\), in meters, that his water bottle is after \(t\) seconds.

1. Complete the table, and then plot the data on the coordinate plane.

   \(t\) (seconds)	\(d\) (meters)
   0
   0.5
   1
   1.5
   2

   

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2. Is the water bottle falling at a constant speed? Explain how you know.

The graph shows how much insulin, in micrograms (mcg), is in a patient's body after receiving an injection. Assume that the amount of insulin continues to decay exponentially.

1. Write an equation giving the number of mcg of insulin, \(m\), in the patient's body \(h\) hours after receiving the injection.
2. After 3 hours, will the patient still have at least 10 mcg of insulin in their body? Explain how you know.

Graph of an exponential function, origin O, with grid. Horizontal axis, time (hours), scale 0 to 2 point 5, by 0 point 5’s. Vertical axis, insulin (mcg), scale 0 to 240, by 20’s. The function is discrete and has these points: (0 comma 200), (1 comma 80), (2 comma 32).