For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on
a certain object, the acceleration of the object is 5 meters per second². If the acceleration of the object becomes 4 meters per second², what is the force?
The question is asking for an exponential function in the form . The goal is to find the value of and such that both and are on the graph of this function.
Saying that a point is on this function is the same as stating that if , then .
is on . Therefore, when , it must be true that . On the other hand, any non-zero number to the th power is . Since (apparently) , . Conclusion: .
is on . Therefore, when , it must be true that . Since it is determined that , . Hence . Take the cube-root of both sides: .