Takumi plants a tree in his backyard and studies how the number of branches grows over time.
He predicts that the relationship between N, the number of branches on the tree, and t, the elapsed time, in years, since the tree was planted can be modeled by the following equation.
N = 5 * 10^0.3t
According to Takumi's model, in how many years will the tree have 100 branches?
Give an exact answer expressed as a base-10 logarithm.
100 = 5 * 10^(0.3t), solve for t
Divide both sides by 5:
Take the log of both sides:
Divide both sides by 0.3:
Multiply the RHS by 10 / 10
t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.