Question

Takumi plants a tree in his backyard and studies how the number of branches grows over

Answer 1

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

Answer 2

Answer:

t = log 20 base 1.003

Step-by-step explanation:

since the tree was planted can be modeled by the following equation.

N = 5(100.3)^t

To calculate the number of years the tree will have 100 branches, we will substitute N for 100 and log both sides

100 = 5(1.003)^t

100 / 5 = (1.003)^t

20 = (1.003)^t

Log both sides

Log20 = log (1.003)^t

Log20 = t log 1.003

t = log 20 / log 1.003

Since both the numerator and denominator are expressed in base 10. Therefore

t = log 20 base 1.003