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

1. The correct option is d.

2. The correct option is c.

Explanation:

The given function is

`f(x)=((1)/(2))^x`

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

`f(-7)=((1)/(2))^(-7)`

`f(-7)=2^(7)`
`[\because ((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)=((1)/(2))^(5)`

`f(5)=(1)/(2^5)`

`f(5)=(1)/(32)`

`f(5)=0.03125`

`f(5)\approx 0.0313`

Therefore the correct option is c.