rate=K[X]^m. Determine the value of m if the rate increases by a factor of 9 when [X] is tripled.

Question

A. Determine the value of m if the rate increases by a factor of 9 when [X] is tripled.

B. Determine the value of m if the rate remains unchanged when [X] is tripled.

Answer 1

rate = k[X]^m

Assume rate is initially a value of 1, so when tripled it becomes a value of 3. k is constant so no need to include in in the calculations.

A). rate increases by a factor of 9 when [X] is tripled

9 = 3^m

m = 2 since 3 squared = 9

B). rate remains unchanged when [X] is tripled

1 = 3^m

m = 0 since 3 to the zero power = 1