Direct variation helps to calculate exponential proportions and is an easy way to figure out relations. If Godzilla were chasing you, which car would you rather pick: the heavier or lighter one? Watch the video to find out.
Suppose that each car's top speed varies directly to the car's weight when it is squared.
For the rest of this problem, assume the following relationship: a car weighing 500 kilograms
would have a top speed of 200 kilometers per hour.
Dario drives a car that weighs 700 kilograms. That's 1,500 pounds...ish.
What's the top speed he can attain as he tries to flee from the monster?
Here are your choices: In this scenario, the heavier a car is, the
faster it can go. Hmm... maybe rocket fuel weighs a lot.
Since the top speed... "T"... varies directly with the weight of the car... "W"...
...the equation relating the two will be "T equals kW squared."
This is exactly what direct variation is -- a relationship between two variables in which
one changes in proportion to the other. The k snuck in there because the top speed
is related proportionally to the square of the weight, but not exactly.
In other words, the weight of the car is not exactly the square of the top speed...
...but the weight of the car squared increases at the same rate as the top speed.
Okay, so we're given two values... ...a top speed of 200 and a weight of 500.
When we plug them into our equation, we get 200 equals k times 500 squared, which equals
k times 250,000. When we divide both sides by 250,000, we are
left with k equals point-zero-zero-zero-eight. Now that we've got our "k," we can just plug
in the value for Dario's 700 kilogram car. T equals point-zero-zero-zero-eight times
700 squared, or... ...T equals 392 kilometers per hour.
We're going to hitch a ride with Answer D. That speed should be enough to get Dario to
safety. Godzilla is scary, but he's not exactly quick
on his feet.