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((1)/(5)\right)^x\to b=3>0\ and\ a=(1)/(5)\in(0,\ 1)\ \ \boxed{!}\\\\II.\ f(x)=\left((1)/(2)\right)^x\to b=1>0\ and\ a=(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

I and III only

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.