Question

consider the function: y=f(x)=(1/2)^x
the values of f(-7) is:
a) 0.0078
b) 0.78
c) 64
d) 128

the value of f(5) rounded to the nearest ten thousand is:
a) 0.0309
b) 0.0312
c) 0.0313
d) 32

Answer 1

1/2^-7=128
(1/2)^5=.0313

Answer 2

Answer:

1. The correct option is d.

2. The correct option is c.

Step-by-step explanation:

The given function is

$f(x)=(\frac{1}{2})^x$

1. To find the value of f(-7) substitute x=-7 in the given function.

$f(-7)=(\frac{1}{2})^{-7}$

$f(-7)=2^{7}$                         $[\because (\frac{1}{a})^{-n}=a^n]$

$f(-7)=128$

Therefore the correct option is d.

2. To find the value of f(5) substitute x=5 in the given function.

$f(5)=(\frac{1}{2})^{5}$

$f(5)=\frac{1}{2^5}$

$f(5)=\frac{1}{32}$

$f(5)=0.03125$

$f(5)\approx 0.0313$

Therefore the correct option is c.