Find a power function that models the data in the table. Round to three decimal places if necessary.
-The population of a small town is given by the table. $\begin{array}{r|rrrr}
\text { Year } & 1980 & 1990 & 2000 & 2010 \
\hline \mathrm{P} & 7500 & 7513 & 7552 & 7617
\end{array}$

If the population is modeled by $\mathrm { p } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } + \mathrm { b }$ where $\mathrm { t }$ is in years and $\mathrm { t } = 0$ corresponds to the year 1980 and $t = 1$ corresponds the year 1990 , find $a$.
A) 26
B) 30
C) 15
D) 13

Question

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The population of a small town is given by the table. $\begin{array}{r|rrrr}
\text { Year } & 1980 & 1990 & 2000 & 2010 \
\hline \mathrm{P} & 7500 & 7513 & 7552 & 7617
\end{array}$

If the population is modeled by $\mathrm { p } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } + \mathrm { b }$ where $\mathrm { t }$ is in years and $\mathrm { t } = 0$ corresponds to the year 1980 and $t = 1$ corresponds the year 1990 , find $a$.
A) 26
B) 30
C) 15
D) 13

Quizplus · Accepted Answer

Given the model $p(t) = at^2 + b$, we can use two points from the table to solve for $a$ and $b$. Let's use the points for 1980 ($t=0$, $p=7500$) and 1990 ($t=1$, $p=7513$). Substituting the first point into the equation gives $7500 = a(0)^2 + b$, which simplifies to $b = 7500$. Substituting the second point gives $7513 = a(1)^2 + 7500$, which simplifies to $a = 7513 - 7500 = 13$.

Find a Power Function That Models the Data in the Table