Chapter 7.6, Problem 69HP

To determine

To write an exponential decay with asymptote of $y=-2$

Answer to Problem 69HP

  $y=2^{-x}-2$

Explanation of Solution

Consider an equation $y=2^{-x}-2$

Calculation for graph:

Consider $y=2^{-x}-2$

Values of x	Values of y
0	-1
-1	0
-2	2
-3	6
-4	12

From the above table the graph can be plotted.

Graph:

  

Interpretation:

From the above graph it is clear that the function is an exponential decay with the asymptote of $y=-2$ .

Conclusion:

Hence, the assumed function satisfies the given condition.