Find the equation for the exponential function f (x) = b .aˣ that passes through the points (0,6) and (1,11).

Answer:[tex]f(x)=6.(1,83)^{x}[/tex]Step-by-step explanation:We have two points (0,6) and (1,11) and to find the exponential function that passes through that points we have to substitute them in the equation [tex]f(x)=b.a^{x}[/tex].Observation: f(x)=y then [tex]y=b.a^{x}[/tex]First we are going to replace the point (0,6) in the equation, where x=0 and y=6.[tex]y=b.a^{x}\\ 6=b.a^{0}[/tex]Remember: [tex]a^{0}=1[/tex][tex]6=b.a^{0} \\6=b[/tex]We got the value of b and it's 6. The equation now is:[tex]y=6.a^{x}[/tex]Finally we have to replace the point (1,11),[tex]y=6.a^{x} \\ 11=6.a^{1} \\ 11=6.a[/tex]Remember: [tex]a^{1}=a[/tex]Isolating the variable a:[tex]11=6.a\\ \frac{11}{6} =a\\1,83=a[/tex]We have then, a=1.83 and b=6. Replacing a and b in [tex]f(x)=b.a^{x}[/tex]We obtain:[tex]f(x)=6.(1,83)^{x}[/tex]