Percentage increase in resistance to motion

[greg_rack]

Homework Statement:

The resistance to the motion of a car is directly proportional to the square of the speed of the car.
The car increases its speed by 20%.
What is the percentage increase in the resistance to the motion of the car?

Relevant Equations:

Percentage increase;

So, I simply used the percentage increase formula for the resistance force, but what I come up with is a 9.5% increase, as opposed to the 44% it should be...
Here's my procedure:

 

[willem2]

It's the square, not the square root.

 

[greg_rack]

It's the square, not the square root.

What a fool! I'm Italian and understanding physics problems isn't always easy 😅... thank you!

 

[Lnewqban]

The resistive force to the movement of your car (and fuel consumption) always grows more rapidly than the speed does.
If the car increases its speed by 20%, naturally the percentage increase in the resistance to its motion should be 44%.