A small college has 2546 students in 1994 and 2702 students in 1996. Assume that the enrollment follows a linear growth pattern. Let t=0 correspond to 1990 and let y(t) represent the enrollment in year t.
a. Question: Assume that y(t) is linear. Using the data given, find the slope of y(t)
b. Question: What does the slope of y(t) signify in terms of enrollment growth?
c. Question: Find an equation for y(t) and use it predict the enrollment of the college in 1999.
a. Question: Assume that y(t) is linear. Using the data given, find the slope of y(t)
b. Question: What does the slope of y(t) signify in terms of enrollment growth?
c. Question: Find an equation for y(t) and use it predict the enrollment of the college in 1999.
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a.
Linear means a straight line. Linear growth means an even amount and in this case it is (2702-2546) 156 per 2 years, which equals 78/yr. This, if plotted on a graph of enrollment versus time, would be the slope of the line.
b.
The slope is constant at 78/yr. The enrolement is directly proportional to the year.
c.
On the basis of 78/yr, we can roll back 4 years (4x78=312) and determine the enrolement in 1990 to be (2702-312) 2390. A graph of enrollment versus time (t), with t=0 being 1990 and sloping upward 78/yr. would satisfy an equation of y(t) = mt + b where m is the slope and b is the y axis intercept. In this problem m=78, b=2390.
y(t)=78t +2390
So for 1999 where t=1999-1990=9
y(for 1999) = 78x9 + 2390 = 3092 enrolement
Linear means a straight line. Linear growth means an even amount and in this case it is (2702-2546) 156 per 2 years, which equals 78/yr. This, if plotted on a graph of enrollment versus time, would be the slope of the line.
b.
The slope is constant at 78/yr. The enrolement is directly proportional to the year.
c.
On the basis of 78/yr, we can roll back 4 years (4x78=312) and determine the enrolement in 1990 to be (2702-312) 2390. A graph of enrollment versus time (t), with t=0 being 1990 and sloping upward 78/yr. would satisfy an equation of y(t) = mt + b where m is the slope and b is the y axis intercept. In this problem m=78, b=2390.
y(t)=78t +2390
So for 1999 where t=1999-1990=9
y(for 1999) = 78x9 + 2390 = 3092 enrolement