SOLUTION: The population of Smalltown, in thousands, t years after 1990 can be modelled using the formula S(t) = 20(t+2)/(t+3) while the population of Little City, in thousands, t years aft

Algebra ->  Rational-functions -> SOLUTION: The population of Smalltown, in thousands, t years after 1990 can be modelled using the formula S(t) = 20(t+2)/(t+3) while the population of Little City, in thousands, t years aft      Log On


   



Question 1071629: The population of Smalltown, in thousands, t years after 1990 can be modelled using the formula S(t) = 20(t+2)/(t+3) while the population of Little City, in thousands, t years after 1990 is L(t) = 240/(10+t). During which years, after 1990, was Smalltown larger than Little City?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+S%28t%29+%3E+L%28t%29+
+20%2A%28+t+%2B+2+%29%2F%28+t+%2B+3+%29+%3E+240%2F%28+10+%2B+t+%29+
+%28+t+%2B+2+%29%2F%28+t+%2B+3+%29+%3E+12%2F%28+10+%2B+t+%29+
Multiply both sides by +%28+t%2B3+%29%2A%28+t+%2B+10+%29+
+%28+t+%2B+10++%29%2A%28+t+%2B+2+%29+%3E+12%2A%28+t+%2B+3+%29+
+t%5E2+%2B+12t+%2B+20+%3E+12t+%2B+36+
+t%5E2+%3E+16+
+t+%3E+4+
1990 + 4 = 1994
-------------------
Smalltown was larger than Little City for
all years after 1994
---------------------
check:
+%28+t+%2B+2+%29%2F%28+t+%2B+3+%29+%3E+12%2F%28+10+%2B+t+%29+
+%28+4.1+%2B+2+%29%2F%28+4.1+%2B+3+%29+%3E+12%2F%28+10+%2B+4.1+%29+
+6.1%2F7.1+%3E+12%2F14.1+
+.8592+%3E+.85106+
You can check to see that
+S%28t%29+%3C+L%28t%29+ when +t+=+3.9+