Given the description, can the situation be modeled by a linear or exponential function. If it is linear describe the common difference or if it is exponential describe the common ratio.
1) You decide to go for a run (you don't change speed) for \( 5 \) miles and it takes you \( 37 \) minutes and \( 30 \) seconds.
2) Bacteria is growing at a rate at which is doubles every \( 20 \) days.
Given the table, determine if the data provided is linear, exponential or neither. If it is linear describe the common difference or if it is exponential describe the common ratio.
3)\( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & 2 & 4 & 6 & 8 & 10 \\ \hline \end{array} \)
4) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & \dfrac{1}{4} & \dfrac{1}{2} & 1 & 2 & 4 \\ \hline \end{array} \)
5) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & 8 & 4 & 2 & 1 & \dfrac{1}{2} \\ \hline \end{array} \)
6) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}3 & \text{-}1 & 0 & 2 & 4 \\ \hline \textbf{f(x)} & \text{-}8 & \text{-}2 & \text{-}1 & \text{-}0.25 & \text{-}0.0625 \\ \hline \end{array} \)
7) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & \text{-}2 & \text{-}1.5 & \text{-}1 & \text{-}0.5 & 0 \\ \hline \end{array} \)
8) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}3 & \text{-}1 & 0 & 2 & 4 \\ \hline \textbf{f(x)} & \text{-}2.5 & \text{-}1.5 & \text{-}1 & \text 0 & 1 \\ \hline \end{array} \)
9) Create a table of values that displays a linear growth with a common difference of \( 2 \).
10) Create a table of values that displays a exponential growth with a common ratio of \( 1.5 \).
1) You decide to go for a run (you don't change speed) for \( 5 \) miles and it takes you \( 37 \) minutes and \( 30 \) seconds.
2) Bacteria is growing at a rate at which is doubles every \( 20 \) days.
Given the table, determine if the data provided is linear, exponential or neither. If it is linear describe the common difference or if it is exponential describe the common ratio.
3)\( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & 2 & 4 & 6 & 8 & 10 \\ \hline \end{array} \)
4) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & \dfrac{1}{4} & \dfrac{1}{2} & 1 & 2 & 4 \\ \hline \end{array} \)
5) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & 8 & 4 & 2 & 1 & \dfrac{1}{2} \\ \hline \end{array} \)
6) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}3 & \text{-}1 & 0 & 2 & 4 \\ \hline \textbf{f(x)} & \text{-}8 & \text{-}2 & \text{-}1 & \text{-}0.25 & \text{-}0.0625 \\ \hline \end{array} \)
7) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}2 & \text{-}1 & 0 & 1 & 2 \\ \hline \textbf{f(x)} & \text{-}2 & \text{-}1.5 & \text{-}1 & \text{-}0.5 & 0 \\ \hline \end{array} \)
8) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & \text{-}3 & \text{-}1 & 0 & 2 & 4 \\ \hline \textbf{f(x)} & \text{-}2.5 & \text{-}1.5 & \text{-}1 & \text 0 & 1 \\ \hline \end{array} \)
9) Create a table of values that displays a linear growth with a common difference of \( 2 \).
10) Create a table of values that displays a exponential growth with a common ratio of \( 1.5 \).
Review
11) Solve the following equation: \( 2x - 4 = 2 - (6 - 3x) \)
12) Graph the line \( y = \frac{1}{2} x + 5 \)
13) Solve the system \( \begin{cases} 2x+9y=\text{-}4\\ x-2y=11\\ \end{cases} \)
Practice Problems Solution Bank
11) Solve the following equation: \( 2x - 4 = 2 - (6 - 3x) \)
12) Graph the line \( y = \frac{1}{2} x + 5 \)
13) Solve the system \( \begin{cases} 2x+9y=\text{-}4\\ x-2y=11\\ \end{cases} \)
Practice Problems Solution Bank