At time t = 0, a seed is planted. After t weeks, the height of the plant is given by $f ( t ) = 0.3 t ^ { 2 } + 0.6 t + 0.5$ inches. At what rate is the plant growing after 8 weeks?
A) 5.4 inches/week
B) 10.1 inches/week
C) 0.6t + 0.6 inches/week
D) 24.5 inches/week
E) none of these

Question

Quizplus · Accepted Answer

The rate at which the plant is growing after 8 weeks is found by taking the derivative of $f(t)$ with respect to $t$, which gives $f'(t) = 0.6t + 0.6$. Substituting $t = 8$ into $f'(t)$ gives $f'(8) = 0.6(8) + 0.6 = 4.8 + 0.6 = 5.4$ inches/week.

At Time T = 0, a Seed Is Planted f(t)=0.3t2+0.6t+0.5f ( t ) = 0.3 t ^ { 2 } + 0.6 t + 0.5f(t)=0.3t2+0.6t+0.5

At Time T = 0, a Seed Is Planted $f ( t ) = 0.3 t ^ { 2 } + 0.6 t + 0.5$