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 pattern

Using the Exponential Modeling knowledge point

$$
LATEXBLOCK0
$$

The ratio of consecutive \(y\)-values is constant:

$$ \frac{1.5}{0.5} = 3, \quad \frac{4.5}{1.5} = 3, \quad \frac{13.5}{4.5} = 3 $$

Determine the exponential equation

Using the Exponential Growth Calculation knowledge point

$$
LATEXBLOCK1
$$

Answer:

The equation that models the given data is:

$$y = 0.5 \cdot 3^x$$