In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.
Find a quadratic model for the data in the table. Type your answer below. show your work.
time hours , 0 1 2 3 4 5 6
Population (1000s) 5. 3.0 1.7 1.1 1.3 2.3 4.0
1 3 2 7 8 5 8
My answer is
at^2+bt+c=p t=time(hrs). P= population(1000’s)
t=1, p=3.03
t=2, p=1.72
t=3, p=1.17
am I right ?
that is not the answer, you need to find a, b, c.
at^2+bt+c=p t=time(hrs). P= population(1000’s)
a+b+c=3.03
4a+2b+c=1.72
9a+3b=c=1.17
??
The following table provides phenotypic data for a population of mammoths living in cold environments based on fossil and DNA evidence.
Characteristic Percent of Population Showing Trait by Generation
Generation 1 Generation 2 Generation 3
Tusks greater than 2.5 m in length 25 25 25
Tusks less than 2.5 m in length 75 75 75
Mass greater than 4,000 kg 15 15 15
Mass less than 4,000 kg 85 85 85
Fur thickness greater than 6 cm 15 25 35
Fur thickness less than 6 cm 85 75 65
Based on this data and your knowledge of natural selection, which explanation best explains the trends seen in the data?
Based on the data, it appears that natural selection is not favoring any particular trait in any of the three generations. The percentage of mammoths showing each trait remains the same across all three generations. This could suggest that the environment has not changed significantly to favor one trait over another, or that genetic drift may be playing a role in maintaining the frequency of each trait. It's also possible that other factors, such as sexual selection or migration patterns, are influencing the traits observed in the population. Therefore, it's difficult to determine a clear explanation for the trends seen in the data based solely on the information provided.
To find a quadratic model for the given data, we need to solve the system of equations for the coefficients a, b, and c in the equation p = at^2 + bt + c.
We are given three data points: (t=1, p=3.03), (t=2, p=1.72), and (t=3, p=1.17).
Step 1: Substitute the given data points into the equation p = at^2 + bt + c.
For the first data point:
3.03 = a(1^2) + b(1) + c
For the second data point:
1.72 = a(2^2) + b(2) + c
For the third data point:
1.17 = a(3^2) + b(3) + c
Step 2: Rewrite these equations in a linear system form.
Equation 1: a + b + c = 3.03
Equation 2: 4a + 2b + c = 1.72
Equation 3: 9a + 3b + c = 1.17
Step 3: Solve the system of equations.
There are multiple ways to solve this system of equations, but one approach is to use matrix methods. Here, we'll use the Cramer's rule to find the values of a, b, and c.
First, let's calculate the determinants of the coefficients:
D = 1*(2*1 - 3*1) - 1*(4*1 - 9*1) + 1*(4*3 - 9*2) = 1 - 5 + 6 = 2
Da = 3.03*(2*1 - 3*1) - 1*(1.72*1 - 1.17*2) + 1*(1.72*3 - 1.17*2) = 0.33 + 2.19 + 2.63 = 5.15
Db = 1*(1*1 - 3*1) - 3.03*(4*1 - 9*1) + 1*(4*3.03 - 9*1.72) = 0.12 - 17.07 + 6.02 = -10.93
Dc = 1*(2*1 - 3*1) - 1*(4*1 - 9*1) + 3.03*(4*1 - 9*2) = 1 - 5 - 32.22 = -36.22
Now we can find the values of a, b, and c:
a = Da/D = 5.15/2 = 2.575
b = Db/D = -10.93/2 = -5.465
c = Dc/D = -36.22/2 = -18.11
Therefore, the quadratic model for the given data is:
p = 2.575t^2 - 5.465t - 18.11
So, your answer is incorrect. The correct quadratic model equation, based on the given data, is p = 2.575t^2 - 5.465t - 18.11