Exercise 43 Page 279

To draw the graph of g(x), we will first make a table of values. We know that g(0)=8, and each term is 2.5 times the previous term.

The ordered pairs (- 1,3.2), (0,8), (1,20), and (2,50) all lie on the function. Now, we will plot and connect these points with a smooth curve.

Let's draw the functions f(x)=0.5(4)^x and g(x) on the same axes and compare them.

We see that both functions have different y-intercepts when x=0. The value of g(x) is greater than the value of f(x) over the rest of the interval.

Showing Our Work

Graphing f(x)

To graph the exponential function f(x)=0.5(4)^x, we will first make a table of values.

x	0.5(4)^x	f(x)=0.5(4)^x
- 1	0.5(4)^(- 1)	0.125
0	0.5(4)^0	0.5
1	0.5(4)^1	2
2	0.5(4)^2	8
3	0.5(4)^3	32

Let's now plot and connect the points ( - 1, 0.125), ( 0, 0.5), ( 1, 2), ( 2, 8), and ( 3, 32) with a smooth curve.