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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

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

Applications and Investigations in Earth Science (9th Edition)
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
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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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.
Transcribed Image Text:# 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.
Transcribed Image Text:### 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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