Respuesta :
Answer:
[tex]$ y = (13)7^x $[/tex]
Step-by-step explanation:
When two points are given say, [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] the exponential function passing through these points is given by
[tex]$ y = ab^x $[/tex]
This is obtained by solving for [tex]$ a $[/tex] and [tex]$ b $[/tex] in
[tex]$ y_1 = ab^{x_1} \hspace{15mm} (1) $[/tex]
[tex]$ y_2 = ab^{x_2} \hspace{15mm} (2) $[/tex]
when we solve (1) and (2) for [tex]$ a $[/tex] and [tex]$ b $[/tex] we substitute it in the main equation to get the desired exponential function.
Here: [tex]$ (x_1, y_1) = (0, 13) $[/tex] and [tex]$ (x_2, y_2) = (2, 637) $[/tex].
Substituting in (1) and (2), we get:
[tex]$ 13 = ab^0 $[/tex]
[tex]$ 637 = ab^2 $[/tex]
From the first equation we get: [tex]$ a = 13 $[/tex] [since [tex]$ b^0 = 1 $[/tex]].
Now substitute a = 13 in the second equation to get the value of b.
[tex]$ \implies 637 = (13)b^2$[/tex]
[tex]$ \implies b^2 = 49 $[/tex] [tex]$ \implies b = 7 $[/tex]
Substituting the values in the main equation we get:
[tex]$ y = (13)7^x $[/tex]
