The graph shows two functions A and B, where one is linear and one is exponential. Between x=1
and x=2
, function A goes from being less than function B to greater than function B. What will happen as the functions continue for x greater than 5? Explain.
As we can see from the graph, function B is exponential and function A is linear. When x is between 1 and 2, function A becomes greater than function B. This could be because the linear function A has a greater rate of increase compared to the exponential function B within this range.
As the functions continue for x greater than 5, the exponential function B will eventually overtake the linear function A. This is because exponential growth accelerates at a faster rate compared to linear growth. Therefore, eventually, the exponential function will grow so rapidly that it will surpass the linear function and continue to diverge further away from it as x increases.