Look at the form of the functions and try to predict their characteristics. Graphing them together can ease the comparison.
See solution.
Practice makes perfect
We are given the exponential functions shown below for us to compare. We will label them in order to tell them apart.
y_1 = 2(5)^x and y_2=5^x
Notice that the first of them is of the form y= ab^x, while the second one is of the form y= b^x.
y &= a b^x &&y = b^x
y_1 &= 2( 5)^x &&y_2= 5^x
Since a= 2>1, we know that y_1 = 2(5)^x is a vertical stretch of y_2=5^x by a factor of 2. We can also find their y-intercepts by evaluating the functions at x=0. Recall that for any nonzero number a, a^0=1.
&y_1( 0) = 2(5)^0 &&y_2( 0)=5^0
&y_1(0) = 2(1) &&y_2(0)=1
&y_1(0) = 2
We can also visualize these differences by graphing both functions together.
From the graph, we can confirm that the function y_1=2(5)^x is a vertical stretch of y_2= 5^x by a factor of 2. We also see that the y-intercept of y_1 is 1, while the y-intercept of y_2 is 2.
