Therefore, for all exponential functions a≠0 and b>0,b≠1.
Graph the function
The points found above all lie on the function. To graph the function, we can plot them in a coordinate plane and connect them with a smooth curve.
This process can be repeated until a general form of the graph emerges.
Lastly, the graph can be drawn by connecting the points with a smooth curve.
In 1976, scientists discovered a rare population of Flemish Giant rabbits in a secluded forest. Since then, they've been monitoring the population. During the five years of the study, the number of rabbits could be modeled with the exponential function shown.
Use the graph to write the rule for the function, then interpret its initial value and constant multiplier.
Use the graph to solve the equation
We can identify one such point in the graph. Let's now find the x-coordinate of this point graphically.
This x-coordinate is not easily read from the graph, so we'll have to make an approximation. It's just a bit bigger than 3, so we'll use 3.1. This means that an approximate solution to the equation is We can verify this by substituting it into equation to see if a true statement is made.
The right-hand side and the left-hand side are approximately equal, so we have indeed found an approximate solution to the equation: