Question

A researcher in the Amazon rain forest has discovered that the growth rate for a certain type of tree is influenced by both rainfall and humidity. The equation for rainfall is! t2 t 81(t) = ő + ģ and the equation for humidity is 82(t) = 2 The equation for the overall growth of the plant is h' (t) = 0.38ı + 82 If the plant's initial height is 3cm, what is its height at t = 5? 11.62 14.51 8.86 15.55

Answer 1

Solution: Given 8:(t)=+ and 8a(t) = 2 Overall growth is given by: (t) = 0.38+32 = $=036+4+2 = n()=** 2 Initial height of plant = h(0) = 3cm Now Integrating: (=f(******2]d - - ( )+ ({}+2+C h(t)=6**+2+C Substituting h(0) = 3, we get : 03 310) h(O)=3=2 + +2(0)+C=C=3 60 160" h(t)= =+* 60 160 +2+3 At t = 5:4(5) = 150+ 3480 +2(3)+3=(15.55 Option (D)