Solve the problem.
-The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.9 \mathrm { t }$ represents the yearly income (or loss) from a real estate investment, where $t$ is time in years. After how many years does income begin to decline? Round to the nearest tenth of a year, if necessary.
A) $9.5$ years
B) $12.7$ years
C) 19 years
D) $8.5$ years

Question

Quizplus · Accepted Answer

The income begins to decline at the vertex of the parabola, which occurs at $ t = -\frac{b}{2a} $. Here, $ a = -0.1 $ and $ b = 1.9 $, so $ t = -\frac{1.9}{2(-0.1)} = 9.5 $ years.

Solve the Problem I(t)=−0.1t2+1.9t\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.9 \mathrm { t }I(t)=−0.1t2+1.9t

Solve the Problem $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.9 \mathrm { t }$