Question

Determine the equation of the exponential function with a common ratio of 2, a horizontal asymptote at y=4, and passing through the point (2,10).

Answer 1

`\bold{y=1.5* 2^x+4}`

Explanation:

Given:

Exponential function with common ratio 2.

Horizontal asymptote at y = 4

Passes through point (2, 10)

To find:

Equation of the exponential function ?

Solution:

Equation for an exponential function may be given as:

`y=ab^x+c`

Where b is the common ratio and

c is the y value of horizontal asymptote.

`(x, y)` are the points on the function.

We are given that:

b = 2

c = 4

Let us put all the given values and find equation.

`y=a* 2^x+4`

Now, let us put
`x = 2, y = 10` to find the value of a.

`10=a* 2^2+4\\\Rightarrow a* 2^2=10-4\\\Rightarrow a* 4=6\\\Rightarrow a =1.5`

`\therefore` the equation of exponential function is:

`\bold{y=1.5* 2^x+4}`