Question

Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.

Answer 1

ANSWER

The graph in option D.

The y-intercept is
$5$

EXPLANATION.

The given function is

$f(x) = 5( {2}^{x} )$

This function is of the form

$f(x) = a( {b}^{kx} ).$
Since
$k > 0$
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
$x = 0$
into the function to obtain,

$f(0)=5( {2}^{0} )$

This will give us,

$f(0)=5( 1 )=5$

Therefore the correct answer is D.