well i am not relly gud at exp reg. i did first two but struggling with rest of those. help me out here plz. and could you plz tell me whther the first 2 are correct or not?
thanks in advance
In another city, the schools vary in size from 200 to 2 000 students. As a result, the
volleyball league is organized into three divisions. The first division is for schools with less than 500 students, the second division is for schools with 500 to 1 000 students, and the third division is for schools with more than 1 000 students.
The table below shows the populations of two schools from 1995 to 2004. School A has a population that declined from 1995 to 2004. School B has a population that grew from1995 to 2004.
1. Use exponential regression equations of the form y = abt, where y is the school
population and t is the number of years after 1995, to model the populations of
School A and School B. Express a to the nearest whole number and b to the
nearest thousandth.
school A :
y = -0.030x + 3.167
log b = -0.030 ----> b = 10^(-0.030) = 0.933
log a = 3.167 ----> a = 10^3.167 = 1469
school B:
y = 0.015x + 2.682
log b = 0.015 ----> b = 10^(0.015) = 1.035
log a = 2.682 ----> a = 10^2.682 = 481
2. Determine, to the nearest tenth of a percent, the average annual rate of increase or
decrease for each school.
School A: 1353(1 - r) ^9 = 755
(1 - r) ^9 = 755 / 1353 = 0.55802
1 - r = (0.55802) ^1/9
r =- 6.2%
School B: 449(1 + r) ^9 = 646
(1 + r)^9 = 646/449 = 1.4388
1 + r = (1.4388)^1/9 = 1.0412
r = 4.2%
3. Assuming the same annual rate of decrease, predict the population of School A
in September 2009. Show the mathematical basis for your prediction.
4. Assuming the same annual rate of increase and using the values of a and b
from the regression equation, predict the calendar year in which the population
of School B reaches 1 000 for the first time. Justify your prediction graphically
and algebraically.
5. Assuming the same annual rates of decrease and increase, predict the calendar
years in which Schools A and B play in the same division of the league. Justify
your prediction mathematically.
6. • Using the same set of axes, sketch the graphs of the regression equations for
the populations of School A and School B as a function of the years after 1995.
• Determine the point of intersection of the two graphs, and explain the
significance of the intersection point in the context of this project.
i did first two but struggling with rest of those. help me out here.
well i am not relly gud at exp reg. i did first two but struggling with rest of those. help me out here plz. and could you plz tell me whther the first 2 are correct or not?
thanks in advance
You have two regression equations of the form .
3. What value of t does 2009 correspond to? Substitute that value into your regression equation for school A to get the value of y.
4. Solve for t for school B. Note that . Now convert t into its corresponding year.
5. Some of the years are obviously 2001, 2002, 2003, 2004 (since they both have 500 - 1000 students in those years and hence compete in the second division).
Now you need to find the values of t for school A for which y > 500 and the values of t for school B for which y < 1000 (note your answer to Q4 ....). The values of t common to both these solutions will give the values of t (and hence the years) for which both schools compete in the second division .....
6. Draw the graphs, perhaps using technology (although you should have been taught how to draw graphs like these by hand). The t-coordinate of the point of intersection corresponds to the time at which both schools have the same numbers of students. To find the t-coordinate of the point of intersection, equate the regression equations for school A and school B and solve the resulting equation for t (you'll probably need to use technology to do this).