Graph the exponential function.
y=5(2)^x

Option A is correct.

Explanation:

Exponential function: The function is given by : .....[1];

where a≠0 is the initial value and base b>0 , b≠1 and x is any real number.

Given: The exponential function:              ......[2]

On comparing  above with  equation [1] we have,

a =5 and b = 2>1

Since, the domain is all Real numbers and the range is all positive real numbers except 0.

To find y-intercept;

Substitute x = 0 to solve for y;

Substitute in [2] we get;

    [Remember any number to the zero power is 1 ].

Therefore, the  graph has a y-intercept at (0,5).

*If b > 1, then, the  graph increases.

or

we can say that the greater the base, b the faster the graph rises from left to right

and  

If 0<b<1 , then the graph decreases.

Therefore, the given exponential function graph  increases because b = 2>1 .

End behavior of the given function ;

As then,

And for then,