Question

the height of a plant over time is shown in the table below. using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?

plant height
\

$$\begin{tabular}{|c|c|} \\hline t, time in months & h, height in inches \\\\ \\hline 1 & 18 \\\\ \\hline 2 & 18.21 \\\\ \\hline 3 & 18.33 \\\\ \\hline 4 & 18.42 \\\\ \\hline 5 & 18.48 \\\\ \\hline 6 & 18.54 \\\\ \\hline \\end{tabular}$$

• 10 months
• 14 months
• 16 months
• 28 months

Explanation:

Perform logarithmic regression on the data

Using the Logarithmic Regression knowledge point

$$ h(t) = a + b \ln(t) $$

Using the data points \((1, 18)\) and \((6, 18.54)\):

$$
LATEXBLOCK0
$$

Thus, the logarithmic model is:

$$ h(t) \approx 18 + 0.3 \ln(t) $$

Verify the model with other data points

Using the Logarithmic Regression knowledge point

$$
LATEXBLOCK1
$$

The model matches the table values perfectly.

Solve for the age when height is 19 inches

Using the Logarithmic Regression knowledge point

$$
LATEXBLOCK2
$$

The best estimate is approximately 28 months.

Answer:

• 10 months
• 14 months
• 16 months
• 28 months (Correct answer)