Respuesta :
B) Notice how you can get the next value multiplying by 4 each time, while x changes by one:
0.5*5=2, 2*4=8, 8*4=32
This function is 4^(x+4)*2 = 512*4^x, 512*4^(-5)=512/1024=0.5, it works!
0.5*5=2, 2*4=8, 8*4=32
This function is 4^(x+4)*2 = 512*4^x, 512*4^(-5)=512/1024=0.5, it works!
Answer:
Option B- Yes; the domain values are at regular intervals and the range values have a common factor 4.
Step-by-step explanation:
Given : The data
(x) -5, -4, -3, -2
(y) 0.5, 2, 8, 32
To find : The data shows an exponential function or not
Solution :
The general form of an exponential form is [tex]y=ab^x[/tex]
To check whether the data give the exponential function we form equation with the help of two points and verify the other two points .
[tex]y=ab^x[/tex]
Let x= -5 and y=0.5
[tex]0.5=ab^{-5}[/tex]
[tex]\frac{0.5}{b^{-5}}=a[/tex] ......[1]
Let x= -4 and y=2
[tex]2=ab^{-4}[/tex]
[tex]\frac{2}{b^{-4}}=a[/tex] .........[2]
Equate LHS because RHS is equal in equation [1] and [2]
[tex]\frac{2}{b^{-4}}=\frac{0.5}{b^{-5}}[/tex]
[tex]\frac{b^{-4}}{b^{-5}}=\frac{2}{0.5}[/tex]
[tex]b=4[/tex]
Put back in [2]
[tex]\frac{2}{4^{-4}}=a[/tex] .
[tex]a=2\times4^4[/tex]
[tex]a=2\times256=512[/tex]
a=512 and b=4
Exponential function - [tex]y=4(512)^x[/tex]
To verify this function put
1) x=-3
[tex]y=512(4)^{-3}[/tex]
[tex]y=\farc{512}{64}[/tex]
[tex]y=8[/tex]
The point satisfied.
2) x=-2
[tex]y=512(4)^{-2}[/tex]
[tex]y=\farc{512}{16}[/tex]
[tex]y=32[/tex]
The point satisfied.
Therefore, The given data is an exponential function [tex]y=4(512)^x[/tex]
The domain values are at regular intervals and the range values have a common factor 4 because b=4 and the change happen but value of b remain same.
Hence, Option B is correct.
Yes; the domain values are at regular intervals and the range values have a common factor 4.
