When an automobile accelerates, the power, P, needed to overcome air resistance varies directly with a power of the speed, v

Question

P=kv^n

Use data to find the scalling exponent and the constant of variation

v 10 20 30 40
p 355 2840 9585 22,720

Answer 1

355=k (10^n)
22720=k(40^n)=k*4^n*(10^n)

divide second equation by first.

22720/355=4^n solve for n.
take log of each side

log22720-log355= n log 4

now, knowing n, solve for k in the first equation.

Answer 2

Thank you