Solve the problem.
-The polynomial function $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.3 \mathrm { t }$ 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) $5.5 \mathrm { yr }$
B) $6.5 \mathrm { yr }$
C) $13 \mathrm { yr }$
D) $8.67 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find when the income begins to decline, we need to find the vertex of the parabola represented by the given quadratic equation, as this point will give us the maximum income. The formula to find the x-coordinate of the vertex (which in this case corresponds to time, $t$) is given by $-\frac{b}{2a}$, where $a = -0.1$ and $b = 1.3$. Plugging these values into the formula gives us $-\frac{1.3}{2(-0.1)} = 6.5$. Therefore, the income begins to decline after 6.5 years.

Solve the Problem I(t)=−0.1t2+1.3t\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.3 \mathrm { t }I(t)=−0.1t2+1.3t

Solve the Problem $\mathrm { I } ( \mathrm { t } ) = - 0.1 \mathrm { t } ^ { 2 } + 1.3 \mathrm { t }$