Question

find the equation that models this data.
time (minutes) 0 1 2 3
height (feet) 0.5 1.5 4.5 13.5
step 1: plot the data points on the graph.
incorrect. you can drag the point to another location.

Explanation:

Step1: Check if it's a linear or exponential relationship

Let \(x\) be time (minutes) and \(y\) be height (feet). Calculate the ratios of consecutive \(y - values\). \(\frac{1.5}{0.5}=3\), \(\frac{4.5}{1.5} = 3\), \(\frac{13.5}{4.5}=3\). Since the ratio is constant, it's an exponential - growth relationship of the form \(y = ab^{x}\).

Step2: Find the values of \(a\) and \(b\)

When \(x = 0\), \(y=0.5\). Substituting into \(y = ab^{x}\), we get \(y=a\times b^{0}=a\), so \(a = 0.5\). We found the common ratio \(b = 3\) in Step 1.

Answer:

\(y=0.5\times3^{x}\)