Question

How do you make an exponential equation with these two points: (1,2) and (0.5,4)

Answer 1

The required  equation is y=8×($( \frac{1}{2} )^{x}$

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 = $ab^{x}$ where, A and B are any real number.

$\frac{x^{m} }{x^{n} } = x^{m-n}$

Now, the points satisfy the equation.

So,

2 = $ab^{1}$ ------- (1) and

4 =  $ab^{0.5}$ ------ (2)

Now (1) ÷ (2) we get,

$\frac{ab }{ab^{0.5} }$ = $\frac{2}{4}$

or, $b^{0.5}$ = $\frac{1}{2}$

or, b = $\frac{1}{4}$ [ by squaring we get]

Now, from (1) we get,

2 = a×$\frac{1}{4}$

or, a = 8

Hence,

The equation is y=8×($( \frac{1}{2} )^{x}$