Answer:
[tex]\bold{y=1.5\times 2^x+4}[/tex]
Step-by-step explanation:
Equation for an exponential function is given as following:
[tex]y=ab^x+c[/tex]
Where b is the common ratio and
c is the horizontal asymptote (y value)
a is the coefficient of exponential term of [tex]x[/tex]
[tex](x,y)[/tex] 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):
[tex]y=a\times 2^x+4[/tex]
We need the value of a. Let us put value of (x,y) as (2,10).
[tex]10=a\times 2^2+4\\\Rightarrow a\times 4 =10-4 =6\\\Rightarrow a =\dfrac{6}{4} =\bold{1.5}[/tex]
So, the final equation of the exponential function is:
[tex]\bold{y=1.5\times 2^x+4}[/tex]
