Answer :
The exponential function which represented by the values in the table is [tex]f(x)=4(\frac{1}{2})^{x}[/tex] ⇒ 3rd answer
Step-by-step explanation:
The form of the exponential function is [tex]f(x)=a(b)^{x}[/tex] , where
- a is the initial value (when x = 0)
- b is the growth/decay factor
- If k > 1, then it is a growth factor
- If 0 < k < 1, then it is a decay factor
The table:
→ x : f(x)
→ -2 : 16
→ -1 : 8
→ 0 : 4
→ 1 : 2
→ 2 : 1
∵ [tex]f(x)=a(b)^{x}[/tex]
- To find the exponential function substitute the value of x and f(x)
by some values from the table to find a and b, at first use the
point (0 , 4) to find the value of a
∵ x = 0 and f(x) = 4
∴ [tex]4=a(b)^{0}[/tex]
- Remember that any number to the power of zero equal 1
except the zero
∵ [tex]b^{0}=1[/tex]
∴ 4 = a(1)
∴ a = 4
Substitute the value of a in the equation
∴ [tex]f(x)=4(b)^{x}[/tex]
- Chose any other point fro the table to find b, lets take (1 , 2)
∵ x = 1 and f(x) = 2
∴ [tex]2=4(b)^{1}[/tex]
∴ 2 = 4 b
- Divide both sides by 4
∴ [tex]b=\frac{2}{4}=\frac{1}{2}[/tex]
- Substitute the value of b in the equation
∴ [tex]f(x)=4(\frac{1}{2})^{x}[/tex]
The exponential function which represented by the values in the table is [tex]f(x)=4(\frac{1}{2})^{x}[/tex]
Learn more:
You can learn more about the logarithmic functions in brainly.com/question/11921476
#LearnwithBrainly
