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×(
`( (1)/(2) )^(x)`

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.

`(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,

`(ab )/(ab^(0.5) )` =
`(2)/(4)`

or,
`b^(0.5)` =
`(1)/(2)`

or, b =
`(1)/(4)` [ by squaring we get]

Now, from (1) we get,

2 = a×
`(1)/(4)`

or, a = 8

Hence,

The equation is y=8×(
`( (1)/(2) )^(x)`