The polynomial function $I ( t ) = - 0.1 t ^ { 2 } + 1.9$ t represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline?
A) 19 yr
B) 9.5 yr
C) 8.5 yr
D) 12.67 yr

Question

Quizplus · Accepted Answer

The income begins to decline after the vertex of the parabola represented by the polynomial function. The vertex can be found using the formula $t = -\frac{b}{2a}$, where $a = -0.1$ and $b = 1.9$. Plugging these values in gives $t = -\frac{1.9}{2(-0.1)} = 9.5$. Therefore, income begins to decline after 9.5 years.

The Polynomial Function I(t)=−0.1t2+1.9I ( t ) = - 0.1 t ^ { 2 } + 1.9I(t)=−0.1t2+1.9

The Polynomial Function $I ( t ) = - 0.1 t ^ { 2 } + 1.9$