Question

HELP! 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

Answer:

$\bold{y=1.5\times 2^x+4}$

Step-by-step explanation:

Equation for an exponential function is given as following:

$y=ab^x+c$

Where b is the common ratio and  

c is the horizontal asymptote (y value)

a is the coefficient of exponential term of $x$

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

Here, we are given that:

Common ratio, b = 2

Horizontal asymptote at y, c = 4

So, the equation becomes (let us put the values of b and c):

$y=a\times 2^x+4$

We need the value of a. Let us put value of (x,y) as (2,10).

$10=a\times 2^2+4\\\Rightarrow a\times 4 =10-4 =6\\\Rightarrow a =\dfrac{6}{4} =\bold{1.5}$

So, the final equation of the exponential function is:

$\bold{y=1.5\times 2^x+4}$