- given the equations, how do I apply it to the data taken?population ecology lab - growth rate of duckweed the amount of fronds on the duckweeds in the fertilized solution and the water solution (control) were recorded over two weekstime intervals: initial ---- 7 days ---- 14 days # Exponential Growth in Duckweed Study## Record Data and Calculate Average Number of Fronds1. **Record Data in Table 1** and calculate the average number of fronds each day.## Equations for Ideal Exponential GrowthExponential growth, the number of fronds, \( N \), at a given time \( t \) is given by **Equation 1**, where:- \( N_0 \) = number of starting fronds- \( r \) = exponential growth rate constantThis can be rearranged to give **Equation 2** where an estimate of doubling time (\( t_2 \)) can be calculated, where \( \ln(2) = 0.693 \).### Equations- **Equation 1**: \( N_t = N_0 e^{rt} \)- **Equation 2**: \( t_2 = \ln 2 / r \)> **Note**: These equations are valid only for ideal exponential growth conditions (Phase B above). For other phases of growth, different sets of equations must be applied to compensate for the lag phase or to allow for senescence and death.## Calculating Growth RateUsing your starting number of duckweed \( N_0 \) and your second number after a week, you can determine the growth rate of the population by rearranging Equation 1 to solve for \( r \) as in **Equation 3**.- **Equation 3**: \( r = (\ln N_t - \ln N_0) / t \)## ApplicationUsing the data from Table 1, calculate the growth rate (\( r \)) and doubling time (\( t_2 \)) of each sample and record in Table 2. ### Study on Duckweed (Lemna Minor) Growth#### Table 1: Number of Fronds of Lemna Minor (Duckweed)| Sample | Group Member | Session 1 Frond Count | Session 2 Frond Count | Session 3 Frond Count ||-------------|--------------|-----------------------|-----------------------|-----------------------|| **Control** | 1 | 3 | 3 | 9 || | 2 | 3 | 3 | 7 || | 3 | 4 | 2 | 5 || | 4 | | | || **Average** | | 3 | 3.5 | 5.75 || **Fertilized** | 1 | 3 | 5 | 16 || | 2 | 2 | 6 | 10 || | 3 | 3 | 6 | 13 || | 4 | 2 | 4 | 15 || **Average** | | 2.5 | 5.25 | 13 |#### Days of Growth| Date | Time | Days of Growth ||------------|------|----------------|| | | 0 days |#### Table 2: Calculations of Growth Rate and Doubling Time for Each Sample of Duckweed Based on Session 2| Sample | Growth Rate (r) | Doubling Time (t₂) ||-------------|-----------------|--------------------|| 1. Control | | || 2. Fertilized | | |*Note: "*HOW DO I APPLY THE CALCULATIONS THEN W/DATA?*" is written as a query for further calculations based on this data.The document is a part of Bio101 Population Ecology Rev. dated 10/18/19, Page 4 of 6.

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Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

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- given the equations, how do I apply it to the data taken?

population ecology lab - growth rate of duckweed

the amount of fronds on the duckweeds in the fertilized solution and the water solution (control) were recorded over two weeks

time intervals: initial ---- 7 days ---- 14 days

# Exponential Growth in Duckweed Study

## Record Data and Calculate Average Number of Fronds

1. **Record Data in Table 1** and calculate the average number of fronds each day.

## Equations for Ideal Exponential Growth

Exponential growth, the number of fronds, \( N \), at a given time \( t \) is given by **Equation 1**, where:
- \( N_0 \) = number of starting fronds
- \( r \) = exponential growth rate constant

This can be rearranged to give **Equation 2** where an estimate of doubling time (\( t_2 \)) can be calculated, where \( \ln(2) = 0.693 \).

### Equations
- **Equation 1**: \( N_t = N_0 e^{rt} \)
- **Equation 2**: \( t_2 = \ln 2 / r \)

> **Note**: These equations are valid only for ideal exponential growth conditions (Phase B above). For other phases of growth, different sets of equations must be applied to compensate for the lag phase or to allow for senescence and death.

## Calculating Growth Rate

Using your starting number of duckweed \( N_0 \) and your second number after a week, you can determine the growth rate of the population by rearranging Equation 1 to solve for \( r \) as in **Equation 3**.

- **Equation 3**: \( r = (\ln N_t - \ln N_0) / t \)

## Application

Using the data from Table 1, calculate the growth rate (\( r \)) and doubling time (\( t_2 \)) of each sample and record in Table 2.

### Study on Duckweed (Lemna Minor) Growth

#### Table 1: Number of Fronds of Lemna Minor (Duckweed)

| Sample | Group Member | Session 1 Frond Count | Session 2 Frond Count | Session 3 Frond Count |
|-------------|--------------|-----------------------|-----------------------|-----------------------|
| **Control** | 1 | 3 | 3 | 9 |
| | 2 | 3 | 3 | 7 |
| | 3 | 4 | 2 | 5 |
| | 4 | | | |
| **Average** | | 3 | 3.5 | 5.75 |
| **Fertilized** | 1 | 3 | 5 | 16 |
| | 2 | 2 | 6 | 10 |
| | 3 | 3 | 6 | 13 |
| | 4 | 2 | 4 | 15 |
| **Average** | | 2.5 | 5.25 | 13 |

#### Days of Growth

| Date | Time | Days of Growth |
|------------|------|----------------|
| | | 0 days |

#### Table 2: Calculations of Growth Rate and Doubling Time for Each Sample of Duckweed Based on Session 2

| Sample | Growth Rate (r) | Doubling Time (t₂) |
|-------------|-----------------|--------------------|
| 1. Control | | |
| 2. Fertilized | | |

*Note: "*HOW DO I APPLY THE CALCULATIONS THEN W/DATA?*" is written as a query for further calculations based on this data.

The document is a part of Bio101 Population Ecology Rev. dated 10/18/19, Page 4 of 6.

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