Answer:
t (years)= (10log 20/log 1000) in base 10
Step-by-step explanation:
N = 5 × 10^0.3t
N = 100 branches
100 = 5 × 10^0.3t
100/5 = 10^0.3t
20 = 10^0.3t
Taking log of both sides
Log 20 base 10 = 0.3t
Log 20 base 10 = (3/10)t
Multiply both sides by 10
10log 20 base 10 = 3t
Recall, log 1000 base 10 = 3
10 Log 20 base 10 = (log 1000 base 10)×t
t = (10Log 20 base 10)/(log 1000 base 10)
t (years)= (10log 20/log 1000) in base 10
The number of years it will take for the tree to have 100branches is (10log 20/log 1000) in base 10
In 4.33 years will the tree have 100 branches.
Given that,
Takumi plants a tree in his backyard and studies how the number of branches grows over,
He predicts that the relationship between N, the number of branches on the tree, and t years, since the tree was planted can be modeled by the following equation.
[tex]N = 10^{0.3t} \times 5[/tex]
We have to determine,
According to Takumi's model, in how many years will the tree have 100 branches?
According to the question,
Equation; [tex]N = 10^{0.3t} \times 5[/tex]
He predicts that the relationship between N, the number of branches on the tree, and t years,
Therefore, the tree has 100 branches in the how many years is,
[tex]\rm N = 10^{0.3t} \times 5\\\\100 = 10^{0.3t} \times 5\\\\\dfrac{100}{5} = 10^{0.3t} \\\\20 = 10^{0.3t}\\\\Taking \ log \ on \ both \ the \ sides \\\\log 20 = log 10^{0.3t}\\\\log20 = 0.3 t \times log 10 \\\\1.30 = 0.3t \times 1\\\\t = \dfrac{1.3}{0.3}\\\\t = 4.33[/tex]
Hence, In 4.33 years will the tree have 100 branches.
For more details refer to the link given below.
brainly.com/question/7578071
