Jana has to solve a system of equations that contains an exponential function and a linear function. she decides to solve graphically and the graph she obtained is shown.
is the complete solution shown? why or why not?
a) yes, since one of the equations is linear the two functions can only intersect once and the intersection point is shown.
b) yes, since the slope of the line is not as great as the rate of change of the exponential the y-values will be greater and they will only intersect one time.
c) no, exponential functions are the fastest growing functions. since this is decay, eventually the exponential will level out where as the line has a constant rate of change. therefore the exponential will eventually have higher y-values than the line. there must be a second intersection point.
d) no, even though the line has a smaller rate of change initially than the exponential, eventually the exponential will have to have a smaller rate of change than the linear since they are the fastest growing functions. given that there must be at least one more intersection point somewhere near y = -1.