In the compound interest formula A=P(1+i)^n. What type of equation is present if i,A,or P are constants rather than variables?
Given `A=P(1+i)^n` .
(1) If `i` is a constant, this is an exponential function `a=b^n` where `b=P(1+i)` , `b` a constant. (In this case, P is a parameter -- unchanging for the given problem)
(2) If `P` is a constant this is still an exponential function of the form `a=b^n` where `b=P(1+i)` , `b` a constant. (In this case `i` is a parameter -- unchanging for the given problem)
(3) If `A ` is a constant the function is a horizontal line. This implies that `P=0,i=-1` or `n=0` .
** Note that we use the word "variable" in different ways throughout mathematics. The common use is for a letter to represent a changing quantity, but sometimes it indicates a static value that changese from problem to problem (a parameter). Some authors regard quantities such as `e,pi,phi` etc... as "variables".
In the equation `y=ax^2+bx+c` , y is a dependent variable, x the independent variable, and a,b,c are parameters.