Which equation represents exponential growth f(x)=4(0.07)^x , f(x)=2(0.44), f(x)=1/2(6)^x, f(x)=7(1/2)^x

Answer:[tex]f(x)=\frac{1}{2}(6)^x[/tex]Step-by-step explanation:An exponential function is of the form [tex]y=ab^{x}[/tex], where,[tex]a\ne 0[/tex].Now, if a > 0 and b > 1, then the exponential function represent exponential growth.If a > 0 and 0 < b < 1, then the exponential function represent exponential decay.Let us check each function now.Option 1: [tex]f(x)=4(0.07)^x[/tex]Here, [tex]a=4,b=0.07[/tex]As 0.07 < 1, the function is exponential decay.Option 2: [tex]f(x)=2(0.44)^x[/tex]Here, [tex]a=2,b=0.44[/tex]As 0.44 < 1, the function is exponential decay.Option 3: [tex]f(x)=\frac{1}{2}(6)^x[/tex]Here, [tex]a=\frac{1}{2},b=6[/tex]As 6 > 1, the function is exponential growth.Option 4: [tex]f(x)=7(\frac{1}{2})^x[/tex]Here, [tex]a=7,b=\frac{1}{2}[/tex]As  [tex]\frac{1}{2}< 1[/tex], the function is exponential decay.Therefore, the equation that represent exponential growth is  [tex]f(x)=\frac{1}{2}(6)^x[/tex]