Question

A nursery sells plants after 6 year of growth. Two seedlings A and B are planted each of height 5 inches whose growth rates are $\frac{dh_{A}}{dt}$ = 0.5 t + 2 and $\frac{dh_{B}}{dt}$ = t + 1 where heights h_A and h_B are in cms and t is the time in years. Then –

• A. The height of the plants are equal at t = 3 (in years)
• B. The height of the plants are equal at t = 4 (in years)
• C. When the plants are sold, their heights are 26 cms and 30 cms for A & B respectively
• D. When the plants are sold, their heights are 26 cms and 29 cms respectively

Answer 1

Answer: (B)

The height of the plants are equal at t = 4 (in years)

Answer 2

h_A = $\frac { \mathrm { t } ^ { 2 } } { 4 }$ + 2t + 5

Qh_A = 5 at t = 0

h_B = + t + 5