Answer:
a) during the first 10 hours of growth the weight will increase 271.8% relative to the initial state ( or 2.718 g)
b) during the first 20 hours of growth the weight will increase 467.1 % relative to the initial state ( or 4.671 g)
Step-by-step explanation:
since the growing rate law is
W'(t) = 0.1 gr/hour * e^(0.1gr/hour* t) , W'(t) [gr/hour]
and following mathematical conventions: W'(t)= dW/dt
then
dW/dt=0.1 e^(0.1t)
∫dW =∫0.1 e^(0.1t) dt
W = e^(0.1t) + C
at the beginning, (time t=0) the weight is W=2 grams .Therefore
2 g = e^(0.1 g/h*0) + C → 2 g = 1 g + C → C = 1 g
then
W = e^(0.1t) + 1 g
at t= 10 hours
W = e^(0.1 g/h*10h) + 1 g = 3.718 g/h
therefore the weight will increase
ΔW = 3.718 g - 1 g = 2.718 g or 271.8% relative to the initial state
for t=20 hours
W = e^(0.1 g/h*20h) + 1 g = 8.389 g/h
thus, the from t= 10 hours to t= 20 hours the weight will increase
ΔW = 8.389 g/h - 3.718 g = 4.671 g or 467.1 %relative to the initial state
