Bill launched a model rocket, and estimated its height h, in feet, after t seconds. His results are shown in the table.

Question

Time, t 0 1 2 3 4
Height, h 0 110 190 240 255

Question
Bill's data can be modeled by the function h of t equals negative 16 t squared plus 128 t.



Which value is the ,begin emphasis,best,end emphasis, prediction for the height of the rocket after 5.5 seconds?

Answer options with 5 options
A.
150 feet

B.
180 feet

C.
220 feet

D.
250 feet

E.
260 feet

Answer 1

To predict the height of the rocket after 5.5 seconds using the given model \( h(t) = -16t^2 + 128t \), we need to substitute \( t = 5.5 \) into the equation.

Calculating \( h(5.5) \):

\[ h(5.5) = -16(5.5)^2 + 128(5.5) \]

First, calculate \( (5.5)^2 \):

\[ (5.5)^2 = 30.25 \]

Now substitute that back into the function:

\[ h(5.5) = -16(30.25) + 128(5.5) \]

Calculating \( -16(30.25) \):

\[ -16(30.25) = -484 \]

Calculating \( 128(5.5) \):

\[ 128(5.5) = 704 \]

Now combine the results:

\[ h(5.5) = -484 + 704 = 220 \]

So, the predicted height of the rocket after 5.5 seconds is 220 feet.

The best prediction for the height of the rocket after 5.5 seconds is: C. 220 feet.