Question

43 Points
I. ƒ(x) = 3 · 5-x
II. ƒ(x) = (1/2)x
III. ƒ(x) = -7ex + 8
Identify the functions which represent exponential decay.
A) I and II only
B) I and III only
C) I, II, and III
D) II and III only

Answer 1

$f(x)=b(a)^x\\\\exponential\ decay\ for\ b>0\ and\ a\in(0,\ 1)\ or\ for\ b<0\ and\ a>1.\\\\I.\ f(x)=3\cdot5^{-x}=3\cdot\left(\dfrac{1}{5}\right)^x\to b=3>0\ and\ a=\dfrac{1}{5}\in(0,\ 1)\ \ \boxed{!}\\\\II.\ f(x)=\left(\dfrac{1}{2}\right)^x\to b=1>0\ and\ a=\dfrac{1}{2}\in(0,\ 1)\ \ \boxed{!}\\\\III.\ f(x)=-7e^x+8\to b<0\ and\ a=e>1\ \ \boxed{!}\\\\Answer:\ C)\ I,\ II\ and\ III.$

Answer 2

Answer:

I and III only

Step-by-step explanation:

I and II only is correct. Exponential decay functions have the form f(x) = abx + c. Function I is already in this form, and function II can be rewritten by changing

1

2

to 2-1, and then getting 2-x.