Answer:Option A is correct.Explanation:Exponential function: The function is given by : [tex]y = ab^x[/tex] .....[1];where a≠0 is the initial value and base b>0 , b≠1 and x is any real number.Given: The exponential function: [tex]y =5 (2)^x[/tex] ......[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; [tex]y= 5(2)^0 = 5\cdot 1 = 5[/tex] [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 [tex]y =5(2)^x[/tex] ; As [tex]x \rightarrow +\infty[/tex] then, [tex]y \rightarrow +\infty[/tex]And for [tex]x \rightarrow -\infty[/tex] then, [tex]y \rightarrow 0[/tex]