Answer:
f(-7)=128, f(5)=0.0312
Step-by-step explanation:
f(x) is the same thing as y, so correctly written its: f(x)=(1/2)^x
plug -7 in for x: f(-7)=(1/2)^(-7)
simplify by doing (1/2) or .5 raised to the power of -7
f(-7)=128
f(5)=(1/2)^5
(.5)^5
=0.0312
Answer:
1) Option 4 - 128
2) Option 2 - 0.0312
Step-by-step explanation:
Given : Expression [tex]Y=f(x)=(\frac{1}{2})^x[/tex]
To find : The value of f(-7) and the value of f(5) rounded to the nearest ten thousandth?
Solution :
The given expression is [tex]Y=f(x)=(\frac{1}{2})^x[/tex]
1) Substitute x=-7
[tex]f(-7)=(\frac{1}{2})^{-7}[/tex]
As [tex](\frac{1}{a})^{-n}=a^n[/tex]
[tex]f(-7)=2^7[/tex]
[tex]f(-7)=128[/tex]
Therefore, Option 4 is correct.
2) Substitute x=5
[tex]f(5)=(\frac{1}{2})^{5}[/tex]
[tex]f(5)=\frac{1}{2^{5}}[/tex]
[tex]f(5)=\frac{1}{32}[/tex]
[tex]f(5)=0.03125[/tex]
[tex]f(5)\approx 0.0312[/tex]
Therefore, Option 2 is correct.
