Answer:
Option 1. [tex]y = 3.5 ^ x[/tex]
Step-by-step explanation:
Exponential functions usually have the following form:
[tex]y = b(a) ^ x[/tex]
Where a and b are real numbers.
b is the coefficient and a is the base. The variable x is the exponent.
In all the options shown, the coefficient is b = 1.
Since the graph of the function has a value close to 10 when x = 2. Then we can discard the options in which the basis of the function is less than 1.
Then we have two options left:
[tex]1) y = 3.5 ^ x\\\\3) y = 2.4 ^ x[/tex]
When [tex]x = 2\ ,\ 2.4 ^ x = 5.76[/tex]
When [tex]x = 2\ \ ,\ 3.5 ^ x = 12.25[/tex]
Notice in the graph that function 3) is greater than 6 when x = 2, while function 1) is close to 12 when x = 2.
Therefore the correct option is the first option.
[tex]y = 3.5 ^ x[/tex]
