Answer:
There will be a 100 branches on tree in approximately 12 years.
Step-by-step explanation:
Concluding part of the question
In how many years will the number of branches be 100?
Solution
N(t)=38 × (9/5) ^ t/7.3
N(t)=38 × (1.8) ^ t/7.3
a) N = 100, t = ?
100 = 38 × (1.8) ^ (t/7.3)
(100/38) = (1.8) ^ (t/7.3)
2.632 = (1.8) ^ (t/7.3)
Taking the natural logarithms of both sides,
In 2.632 = In [(1.8) ^ (t/7.3)]
0.9676 = (t/7.3) × In 1.8
0.9676 = (t/7.3) × 0.5878
t = (0.9676 × 7.3) ÷ 0.5878
t = 12.02 years = 12 years.
Hope this Helps!!!