SOLUTION: In 2004, in-state tuition at Stanford was $6,092. In 2013, in-state tuition was $9,992. If the cost of in-state tuition C is a linear function of time t, where t represents the num

Algebra ->  Linear-equations -> SOLUTION: In 2004, in-state tuition at Stanford was $6,092. In 2013, in-state tuition was $9,992. If the cost of in-state tuition C is a linear function of time t, where t represents the num      Log On


   



Question 1087075: In 2004, in-state tuition at Stanford was $6,092. In 2013, in-state tuition was $9,992. If the cost of in-state tuition C is a linear function of time t, where t represents the number of years since 2004, write the linear function C(t).

Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For the year 2004, +t+=+0+
For the year 2013, +t+=+9+
-------------------------------
Use the general point-slope formula
+%28+C+-+6092+%29+%2F+%28+t+-+0+%29+=+%28+9992+-+6092+%29+%2F+%28+9+-+0+%29+
+%28+C+-+6092+%29+%2F+t+=+3900+%2F+9+
Multiply both sides by +9t+
+9%2A%28+C+-+6092+%29+=+3900t+
+9C+-+54828+=+3900t+
+9C+=+3900t+%2B+54828+
+C+=+%28+1300%2F3+%29%2At+%2B+6092+
-------------------------------
Check:
does it go through ( 9, 9992 ) ?
+C+=+%28+1300%2F3+%29%2At+%2B+6092+
+C+=+%28+1300%2F3+%29%2A9+%2B+6092+
+C+=+3900+%2B+6092+
+C+=+9992+
OK
does it go through ( 0, 6092 ) ?
+C+=+%28+1300%2F3+%29%2At+%2B+6092+
+C+=+%28+1300%2F3+%29%2A0+%2B+6092+
+C+=+6092+
OK

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

In 2004, in-state tuition at Stanford was $6,092. In 2013, in-state tuition was $9,992. If the cost of in-state tuition C is a linear function of time t, where t represents the number of years since 2004, write the linear function C(t).
With t being time in 2004 (year 0), and tuition in 2004 being $6,092, we get the point: (0, 6,092).  
With t being time (from 2004 to 2013), and tuition in 2013 being $9,992, we get the point: (9, 9,992).
m, or slope =
y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29
y+-+%226%2C092%22+=+%28%221%2C300%22%2F3%29%28x+-+0%29 <====== Applying the POINT-SLOPE form, substituting
y+=+%28%221%2C300%22%2F3%29x+%2B+%226%2C092%22
------- Substituting C(t) for y, and t for x