ANSWER
The graph in option D.
The y-intercept is
[tex]5[/tex]
EXPLANATION.
The given function is
[tex]f(x) = 5( {2}^{x} )[/tex]
This function is of the form
[tex]f(x) = a( {b}^{kx} ).[/tex]
Since
[tex]k > 0[/tex]
the graph of this function will approach positive infinity as the values of x increases without bounds.
This means the graph of this function rises dramatically as the values of x becomes bigger and bigger.
While the graph approaches zero for infinitely smaller values of x. This means that, the graph is asymptotic to the negative x-axis.
For the y-intercept of this graph, we put
[tex]x = 0[/tex]
into the function to obtain,
[tex]f(0)=5( {2}^{0} )[/tex]
This will give us,
[tex]f(0)=5( 1 )=5[/tex]
Therefore the correct answer is D.
