Respuesta :

pierinagiusiano

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]

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