Question

determining data relationships

find the equation that models this data.

\

$$\begin{tabular}{|c|c|c|c|c|} \\hline time (minutes) & 0 & 1 & 2 & 3 \\\\ \\hline height (feet) & 0.5 & 1.5 & 4.5 & 13.5 \\\\ \\hline \\end{tabular}$$

step 1: plot the data points on the graph.

Explanation:

Identify the data points

Using the Exponential Function Properties knowledge point

$$ (x, y) \in \{(0, 0.5), (1, 1.5), (2, 4.5), (3, 13.5)\} $$

Determine the model type

Using the Exponential Growth Calculation knowledge point

$$
LATEXBLOCK0
$$

Write the exponential equation

Using the Exponential Function Properties knowledge point

$$
LATEXBLOCK1
$$

Answer:

The equation that models the given data is:

$$y = 0.5(3)^x$$