College Algebra & Trigonometry, 2018a

3.1. EXPONENTIAL AND LOGISTIC APPLICATIONS 143
through the point (0, 1) on the graph. This is because 1.5 0 =1, 2 0 =1, 3 0 =1and
10 0 =1. Therefore the point where x is 0 and y is 1 is on all four of the graphs.
Although all four of the graphs pass through the point (0, 1), they each do this
in a different way. Let’s look at the slope of a line tangent to each curve at the
point (0, 1). This is the straight line that touches the curve at the point (0, 1), but
nowhere else:
20
15
10
20
15
10
y =2 x
y =1.5 x −4 −2 2 4
5
5
−4 −2 2 4
−5
20
15
10
−5
20
15
10
y =10 x
y =3 x −4 −2 2 4
5
5
−4 −2 2 4
−5
−5
We can see that the slopes of these tangent lines are all different. In the case of
y =2 x , the slope of the tangent line at (0, 1) is about 0.7, while for the graph of
y =3 x , the slope of the tangent line at (0, 1) is about 1.1.