Is the following graph exponential growth or decay?
Hint
Are the y values increasing or decreasing "without bound"?
Answer
Exponential growth. Even though the function is decreasing very sharply, the y values are increasing negatively and they are not leveling out.
Example 2
Is the following graph exponential growth or decay?
Hint
Look left to right. Are the y values leveling out?
Answer
Exponential decay. Even though the function is increasing in y values as you look from left to right, the y values are climbing towards -4. Left to right, if the y values go to a horizontal asymptote, then, ladies and gentlemen, we have decay.
Example 3
What is the horizontal asymptote of the graph below?
Hint
Imagine drawing a horizontal line that the graph looks like it is touching. What is the equation of that line? You've got this!
Answer
y = 1
Example 4
Is the following graph exponential growth or decay?
Hint
Read the graph left to right. Are your eyes going up, down or staying steady.
Answer
Exponential growth. You looked up, didn't you?
Example 5
Graph f(x) = 0.2(4)x.
Hint
Use an table. Plug different values in for x and get y values. Try these x values: -4, -3, -2, -1, 0, 1, 2, 3, 4. Then, graph these on a grid.
table. Plug different values in for x and get y values. Try these x values: -4, -3, -2, -1, 0, 1, 2, 3, 4. Then, graph these on a grid. 