The required equation is y=8×([tex]( \frac{1}{2} )^{x}[/tex]
Step-by-step explanation:
Given,
The two points are (1,2) and (0.5,4)
To find the exponential equation of these given points.
Formula
The general form of exponential equation is y = [tex]ab^{x}[/tex] where, A and B are any real number.
[tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex]
Now, the points satisfy the equation.
So,
2 = [tex]ab^{1}[/tex] ------- (1) and
4 = [tex]ab^{0.5}[/tex] ------ (2)
Now (1) ÷ (2) we get,
[tex]\frac{ab }{ab^{0.5} }[/tex] = [tex]\frac{2}{4}[/tex]
or, [tex]b^{0.5}[/tex] = [tex]\frac{1}{2}[/tex]
or, b = [tex]\frac{1}{4}[/tex] [ by squaring we get]
Now, from (1) we get,
2 = a×[tex]\frac{1}{4}[/tex]
or, a = 8
Hence,
The equation is y=8×([tex]( \frac{1}{2} )^{x}[/tex]
