Solve the problem
-The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.8 \mathrm { t }$ 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) $8 \mathrm { yr }$
B) $18 \mathrm { yr }$
C) $12.00 \mathrm { yr }$
D) $9 \mathrm { yr }$

Question

Quizplus · Accepted Answer

The income begins to decline after reaching the maximum point, which is at the vertex of the parabola. The vertex for a quadratic function $ax^2 + bx + c$ is at $t = -\frac{b}{2a}$. Here, $a = -0.1$ and $b = 1.8$, so $t = -\frac{1.8}{2(-0.1)} = 9$. Thus, income begins to decline after 9 years.

Solve the Problem -The Polynomial Function I(t)=−0.1t2+1.8t\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.8 \mathrm { t }I(t)=−0.1t2+1.8t

Solve the Problem
-The Polynomial Function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.8 \mathrm { t }$