Question

Choose among these options the one that results in a graph that shows exponential decay. A. f(x) = 0.6(2)x B. f(x) = 3(0.7)x C. f(x) = 0.4(1.6)x D. f(x) = 20(3)x

Answer 1

B. f(x) = 3(0.7)ˣ
Decay means an overall decrease in the original value. Exponential equations are written in the form:
amount after time n = original amount x (decay OR increase factor)ⁿ
The value of the factor is less than one in the case of a decay.

Answer 2

Answer:  [B]:  " f(x) = 3(0.7)ˣ " .
________________________________________________________
x  | y         
0 | 3
1  | 2.1
2 | 1.48
_________________________________________________________
When, "x" [which is the exponent] increases" ; the resulting value; "y" on a graph, DECREASES;  hence; "exponential decay". 
_____________________________________________
Consider Choice [A]:  " f(x) = 0.6(2)ˣ " .
_________________________________________________________
x  | y         
0 | 0.6
1  | 1.2
2 | 2.4 ;

When "x" [the exponent] increases, the resulting value; "y" (on a graph); INCREASING;  indicating 'exponential growth' ; NOT 'exponential decay' .
______________________________________________________
Consider Choice [C]:  "f(x) = 0.4(1.6)ˣ " .
_________________________________________________________
x  | y         
0 | 0.4
1  | 0.64
2 | 1.024

When "x" [the exponent] increases, the resulting value; "y" (on a graph); INCREASING;  indicating 'exponential growth' ; NOT 'exponential decay' .

→ As such, Choice: [C]:  is incorrect.
______________________________________________________
Consider Choice [D]:  " f(x) = 20 * (3)ˣ  " ; 
_________________________________________________
x  | y         
0 | 20
1  | 60
2 | 180 ;
_________________________________________________

When "x" [the exponent] increases, the resulting value; "y" (on a graph); INCREASING;  indicating 'exponential growth' ; NOT 'exponential decay;.

→ As such, "Choice [D]" is incorrect.
______________________________________________________