Analyzing the Relationship Between GPA & TV Hours & Solving Real-World Problems

[mkou528]

GPA, G 3.8 3.5 2.3 3 2.8
Hours of TV, H 1.1 1.1 1.7 1.3 1.4

Problem #1 - The table shows the results of an experiment to determine if there is a relationship between the numbers of hours of television watched per day, H, and the GPA, G, of students.
a) Find a linear model that represents the data
b) What is the linear correlation coefficient? Are they any correlation between the variables?
c) Use your model to predict the GPA of a student who watches 2.5 hours of reality shows per day.

** The only thing that I know about this problem is that I’m supposed to scatter plot it on by TI-89, but I don’t know how to do that either.

Problem # 2 – In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again. The data is recorded as follows:

[Time in hours 0 1 2 3 4 5 6
Population in 1000s] 7.62 6.16 5.5 5.64 6.5 8.32 10.86

a) Find a quadratic model that represents the data
b) What is the R2 value? Is the model a good fit?
c) Use your model to estimate the number of bacteria in 8 hours
d) Use your model to estimate the minimum number of bacteria and approximate at what hour the minimum occurred

Problem #3 – P= -2x^2 + 8x –3 where x is the number of units produced in thousands and Profit, P, in hundreds of dollars

a) How many units must be produced to obtain a profit of $500?
b) How many units must be produced to obtain a maximum profit?
c) What is the Maximum profit?


Problem #4 – Consider the function f(x)= (4x-4)/(x^2-2x-24)

a) Find the domain of the function.
b) Find the asymptotes of the function, if it has any.
c) Find the intercepts of the function, if it has any.

Problem # 5 – A state game commission is introducing 100 wolves into a remote area which has previously been uninhabited by wolves. The population of the pack is given by P=[20(5+2t)]/(1+0.06t) where t is the time in years since the introduction. What is the limiting size of the population as time increases?

 

[courtrigrad]

For the first problem, type in the GPA and # of hours in 2 separate lists (L1 and L2). Then do LinReg for L1 and L2. You should get an equation. Remember that in the equation

y-hat = a + bx, b is the correlation coefficient. r is an indicator to how close the set of points of the data is to the predicted line. r^2, the coefficient of determination, sees how much of the data is explained by the linear regression equation on x. For example:

r^2 = 0.87

means that 87% of the data can be explained by the linear regression equation on X. For your other part, just plug in 2.5 hours into your linear regression equation. When you scatterplot this data, and the linear regression equation, you will get an idea of how good a fit the line is. Use this as an example for your other problems.

For #3 just put P = 500 and solve the quadratic. For the other parts I'll give you a hint: -b / 2a is the vertex of a parabola.

For #4: Remember domain can't include anything that will make function undefined, or denominator 0. x^2 - 2x - 24 is in the denominator, so it can't equal 0.

Solve this equation and exclude these values. Asymptotes are defined as:

Horizontal ( lim f(x) = a ) limit as x approaches + or - infinity equals a. For vertical asymptotes:

lim f(x) = +/- 00. Use this as a guide
x --> +/- a
x --> +/ -00

Intercepts you should know when you plug in 0 for x to get y intercepts and vice versa. For your last problem what is the limit as t approaches infinity?

 

[mkou528]

How do you do LinReg for scatter plots on the TI-89? I need this step by step.

Also, does anyone know how to do Problem 5?