Question

The ordered pairs (-2,18) and (-1,6) are solution to exponential equation

Answer 1

Answer:

$f(x) = 2(0.333)^{x}$

Step-by-step explanation:

Let the exponential equation is $f(x) = a(b)^{x}$ ......... (1)

Now, the ordered pairs (-2,18) and (-1,6) are the solution to the exponential equation and they will satisfy the equation (1).

Then, $18 = a(b)^{- 2}$ .......... (2) and

$6 = a(b)^{- 1}$ ........... (3)

Now, dividing equation (3) by equation (2) we get

$\frac{6}{18} = b^{[- 1 - (- 2)]}$

⇒ b = 0.333

Now, from equation (3) we get

$6 = a(0.333)^{- 1} = 3a$

⇒ a = 2

Therefore, the exponential function is $f(x) = 2(0.333)^{x}$. (Answer)