Ann plants some acorns. She figures that as the tree grows, the cells will divide in such a way that the rate of change of the tree's mass will be directly proportional to the mass. She digs up a seedling after 3 months and finds that the mass of the roots/trunks/leaves is 200 grams. The original acorn were 70 grams.
1. Write an equation.
2. How long after the acorn was planted will the oak tree reach 50 kg?
3. predict mass of oak 1, 2, 3 years after the acorn was planted.
4 use the results of 3. to prove the oak grows by a constant factor each year
5. Explain to ann why her model would not give reasonable answers for the tree's mass after many years.
This is my work for part 1. dM/dt=kM, (skipping a few steps) I get M=Ce^kt
As M=70 when t=0, C=70
As M=200 when t=3, I solved M=70e^3k to get k=0.3499
M=70e^0.3499t (M is the mass)
For part 2, I converted 50kg to g, then I solved this equation 70e^0.349t=50000
I get t=304.22 (months)
Part 3 I plug in 12, 24, 36 for t
But I don't know how to do 4 and 5, help?