Question

How many days would it take for a crepe myrtle tree to grow 1 \(\mathrm{cm}\) in height if it grows \(3.38\) feet per year? (Report your answer to three significant figures)

Short answer

It would take 3.55 days for the crepe myrtle tree to grow 1 cm in height.

Step-by-step solution

- Convert growth rate to feet per day

First, convert the annual growth rate from feet per year to feet per day. There are 365 days in a year, so divide the annual growth rate by 365.

- Perform the conversion

The conversion is as follows: \ \( \text{Daily growth rate} = \frac{3.38 \text{ feet/year}}{365 \text{ days/year}} = 0.00926 \text{ feet/day} \). Keep the calculation to three significant figures.

- Convert feet per day to centimeters per day

Next, we need to convert the daily growth rate from feet per day to centimeters per day. Use the conversion factor: 1 foot = 30.48 cm.

- Perform the conversion

The conversion is as follows: \( 0.00926 \text{ feet/day} \times 30.48 \text{ cm/foot} = 0.282 \text{ cm/day} \).

- Calculate the number of days to grow 1 centimeter

Divide the target growth (1 cm) by the daily growth rate in cm/day: \( \frac{1 \text{ cm}}{0.282 \text{ cm/day}} = 3.55 \text{ days} \).

Key concepts

Unit Conversion

Unit conversion is a critical skill in chemistry and many other sciences. It involves changing a measurement from one unit to another using a conversion factor. For example, in our crepe myrtle tree problem, we started with the growth rate in feet per year and needed to convert it to feet per day. To do this, we used the known fact that there are 365 days in a year. The converted rate was then used in subsequent calculations. Understanding how to properly use conversion factors can help students solve a variety of problems where measurements are given in different units.

Significant Figures

Significant figures are the digits in a number that are reliable and necessary to indicate the precision of that number. In scientific calculations, we must often round numbers to the correct number of significant figures. For our problem, where we calculated daily growth rate, it was crucial to maintain three significant figures throughout the solution to ensure accuracy. When you perform calculations, always keep track of significant figures to properly report your results.

Growth Rate Calculations

Growth rate calculations measure how quickly something changes over a specific period. In the crepe myrtle tree problem, the growth rate was provided in feet per year. We converted this to feet per day to understand the tree's daily growth. Such conversions are essential for analyzing and interpreting data for trends over different time frames. Growth rates can apply to various contexts, from biology and ecology to economics.

Measurement Conversions

Measurement conversions are fundamental to solving many science problems. In this case, we converted feet per day to centimeters per day. Using the conversion factor 1 foot = 30.48 cm, we determined the tree's growth rate in centimeters per day. Measurement conversions often require these factors, which can be found in reference materials or through memorization. Accurate conversions ensure that measurements are consistent and comparable across different units.