SOLUTION: The function I(t) = -0.11 + 1.6t represents the yearly income (or loss) from real estate investment, where t is time in years. After what year does income begin to decline? Round t

Algebra ->  Linear-equations -> SOLUTION: The function I(t) = -0.11 + 1.6t represents the yearly income (or loss) from real estate investment, where t is time in years. After what year does income begin to decline? Round t      Log On


   

Question 1158349: The function I(t) = -0.11 + 1.6t represents the yearly income (or loss) from real estate investment, where t is time in years. After what year does income begin to decline? Round the answer to the nearest tenth.
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Asking when at function value begins to decline when the function is linear makes on sense. A linear function is either constant, or always increasing, or always decreasing.

This function is always increasing....

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The function I(t) = -0.11 + 1.6t represents the yearly income=> I have noticed you have linear equation; there is no certain point where a line decline
I assume you have:
I%28t%29+=+-0.1t%5E2+%2B+1.6t+ which is a parabola that have a maximum at vertex
so, write equation in vertex form:


I%28t%29+=+%28-0.1t%5E2+%2B+1.6t%29+....factor out -0.1
I%28t%29+=+-0.1%28t%5E2-+16t%29+........complete square
I%28t%29+=+-0.1%28t%5E2-+16t%2Bb%5E2%29-%28-0.1%29b%5E2+.....b=16%2F2=8
I%28t%29+=+-0.1%28t%5E2-+16t%2B8%5E2%29%2B0.1%2A8%5E2+
I%28t%29+=+-0.1%28t-+8%29%5E2%2B0.1%2A64+
I%28t%29+=+-0.1%28t-+8%29%5E2%2B6.4+
=> h=8 and k=6.4=> vertex is at (8,6.4)
a maximum will be at 8 years, and after 8 years income will begin to decline