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
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
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
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.