Question

Write an exponential function in the form y = a that goes through points ( 0 , 13 ) and ( 2 , 637 )

Answer 1

Answer:

$y = (13)7^x$

Step-by-step explanation:

When two points are given say, $(x_1, y_1)$ and $(x_2, y_2)$ the exponential function passing through these points is given by

                                               $y = ab^x$

This is obtained by solving for $a$ and $b$ in

$y_1 = ab^{x_1} \hspace{15mm} (1)$

$y_2 = ab^{x_2} \hspace{15mm} (2)$

when we solve (1) and (2) for $a$ and $b$ we substitute it in the main equation to get the desired exponential function.

Here: $(x_1, y_1) = (0, 13)$ and $(x_2, y_2) = (2, 637)$.

Substituting in (1) and (2), we get:

$13 = ab^0$

$637 = ab^2$

From the first equation we get: $a = 13$  [since $b^0 = 1$].

Now substitute a = 13 in the second equation to get the value of b.

$\implies 637 = (13)b^2$

$\implies b^2 = 49$  $\implies b = 7$

Substituting the values in the main equation we get:

  $y = (13)7^x$