Answer:
[tex]\bold{y=1.5\times 2^x+4}[/tex]
Step-by-step 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:
[tex]y=ab^x+c[/tex]
Where b is the common ratio and
c is the y value of horizontal asymptote.
[tex](x, y)[/tex] are the points on the function.
We are given that:
b = 2
c = 4
Let us put all the given values and find equation.
[tex]y=a\times 2^x+4[/tex]
Now, let us put [tex]x = 2, y = 10[/tex] to find the value of a.
[tex]10=a\times 2^2+4\\\Rightarrow a\times 2^2=10-4\\\Rightarrow a\times 4=6\\\Rightarrow a =1.5[/tex]
[tex]\therefore[/tex] the equation of exponential function is:
[tex]\bold{y=1.5\times 2^x+4}[/tex]
