Factors that effect population growth are birth rate, life expectancy, and the e
ID: 3102886 • Letter: F
Question
Factors that effect population growth are birth rate, life expectancy, and the environment. Here we will conduct an experiment to model population growth using
m&m candies.Start with 4 m&ms in cup spill them out and if it lands with m side up assume it is male and vice versa. Then for the next round, assume that each female gives birth to another m&m- so, increase the population by an amount equal to the number of females.
My data is:
time pop # females increase
0 4 +2
1 6 + 1
2 7 +2
3 9 +4
4 13 +6
5 14 +12
6 21 +22
****You don't have to mess w/ m&ms I did that it is in table, I need graph and questions 1-5 Please!!!!
1. Display data in scatterplot: pop up left side starting with 10 to 60 on y axis, x axis is time and 1 to 6.
2. Determine an exponential equation of the form f(x)=a*b^x that approximates the population when time (x) is known.
3. using your population function find f(10) and f(12) interpret the results in terms of population.
4. According to your function, when would the population exceed 1000 people (m&ms)
5. when would the population reach 30,000? why would predicting this value be questionable?
Explanation / Answer
1. I can't seem to insert a diagram, so i'll walk you thru the plot. in the scatterplot, plot these points (0,4), (1,6), (2,7), (3,9), (4,13), (5,14), (6,21).
2. for your curve, take two points, i took (2,7) and (6,21). equation is y=ab^x. use the first point. let y=7 and x=2 and solve for a=7/(b^2). use second point. let y=21 and x=6 and sub in the a we just found using the first poing to get 21=[7/(b^2)]b^6. solve and get b=1.31607 and a=4.04 so you equation is
y=(4.04)(1.3)^x
3. using the equation above, let x=10, so then y solves to be 55.7 so the this is saying at year 10 you should have a population of 55. now let x=12, y solves to be 94.1, this means at year 12 you should have a population of 94.
4. you want to find x when y =1000. use the equation above and solve for x to be about 21 but you want the population to EXCEED 1000 so your x is 22 years.
5. same as question 4 but set y=30,000. x=34. this is questionable because your sample size is very small compared to 34 years. therefore the equation derived from your sample size is not representative over a long period of time.
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