Question

Takumi started studying how the number of branches on his tree changes over time.

Answer 1

Answer:

Grows, Factor of 2

Step-by-step explanation:

The relationship between the elapsed time, t, in years, since Takumi started studying his tree, and the total  number of its branches, N(t), is modeled by the function:

$N(t) = 63. 2^t$

For illustration, let us take the growth for the first three years after he started studying the number of branches.

$When \:t=1, N(1) = 63. 2^1=126\\When \:t=2, N(2) = 63. 2^2=252\\When \:t=3, N(3) = 63. 2^3=504\\504\div 252=252\div 126=2$

We notice that for each subsequent year, the number of branches doubles.

Therefore:

Every year, the number of branches  grows by a factor of 2.