I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)------Population
0-----------------------500
1-----------------------600
2-----------------------720
3-----------------------864
4----------------------1037
5---------------------1244
6---------------------1493
7----------------------1792
8---------------------2150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days.
1.) Creating a scatter plot using a graphing calculator:
To create a scatter plot of the given data using a graphing calculator, follow these steps:
- Enter the values for the time and population into lists on your calculator. Let's use List 1 for time and List 2 for population.
- Input the values from the table into the respective lists. For example, in List 1, enter 0, 1, 2, 3, and so on for time, and in List 2, enter 500, 600, 720, 864, and so on for population.
- Go to the graphing menu on your calculator and select the scatter plot option.
- Choose the lists that contain the time and population data.
- Set your window settings according to the provided values: Xmin = 0, Xmax = 10, Xscl = 1, Ymin = 0, Ymax = 2500, Yscl = 100, Xres = 1.
- Plot the graph.
2.) Determining an exponential equation to represent the population without using a graphing calculator:
To determine an exponential equation to represent the population as a function of time, we need to examine the growth pattern of the population.
In an exponential growth model, the population increases by a fixed percentage over a fixed period. In this case, the population is increasing each day by an amount, which indicates exponential growth.
To find the exponential equation, we need to determine the growth constant or percentage increase. Here's how you can do it:
- Calculate the growth factor by finding the ratio of population on subsequent days to the population on the previous day.
- Divide the population on each day by the population on the previous day. For example, divide 600 by 500, then divide 720 by 600, and so on.
- Note the pattern or average growth factor.
In this case, the growth factor appears to be around 1.2, which means the population is increasing by 20% each day.
Now, to determine the exponential equation, we can use the formula:
Population = Initial Population * (1 + Growth Factor)^Time
- The initial population is given as 500.
- The growth factor is 1.2 (20% increase each day).
- The time is the number of days.
So, the exponential equation representing the population as a function of time is:
Population = 500 * (1.2)^Time
3.) Estimating the population of the colony at 10 days:
To estimate the population when the time is 10 days, use the exponential equation obtained in the previous step.
Substitute the value of time (10) into the equation:
Population = 500 * (1.2)^10
Calculating this, the estimated population of the colony at 10 days would be approximately 9312.