Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table lists the distance traveled by a falling object, where t is the elapsed time in seconds and d is the distance in meters. $\begin{array}{r|rrrrrr}
\mathrm{t} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{d} & 0 & 4.9 & 19.6 & 44.1 & 78.4 & 122.5
\end{array}$

\text { If the distance is modeled by } \mathrm { d } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } \text {, find the distance traveled after } 13 \text { seconds. }
\end{array}\]
A) 828.1 meters
B) 2704 meters
C) 676 meters
D) 4057.69 meters

Question

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table lists the distance traveled by a falling object, where t is the elapsed time in seconds and d is the distance in meters. $\begin{array}{r|rrrrrr}
\mathrm{t} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{d} & 0 & 4.9 & 19.6 & 44.1 & 78.4 & 122.5
\end{array}$

\text { If the distance is modeled by } \mathrm { d } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } \text {, find the distance traveled after } 13 \text { seconds. }
\end{array}\]
A) 828.1 meters
B) 2704 meters
C) 676 meters
D) 4057.69 meters

Quizplus · Accepted Answer

The distance traveled by a falling object can be modeled by the equation $d(t) = at^2$, where $d$ is the distance in meters and $t$ is the time in seconds. Given the data, we can see that the distance quadruples when the time is doubled (e.g., from 1 to 2 seconds, the distance goes from 4.9 to 19.6 meters, which is roughly a factor of 4). This pattern is consistent with the equation $d(t) = 4.9t^2$, where $a = 4.9$. To find the distance traveled after 13 seconds, we substitute $t = 13$ into the equation to get $d(13) = 4.9(13)^2 = 4.9 \times 169 = 828.1$ meters.

Find a Power Function That Models the Data in the Table