Question

The ordered pairs (2, 20) and (3, 40) are solutions to an exponential function. Write the equation for this function.

Answer 1

Answer:

The exponential function will be  $f(x) = 5(2)^{x}$

Step-by-step explanation:

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

Now, ordered pairs (2,20) and (3,40) are the solution of the above exponential function. So, they will satisfy the equation.

Now, for the ordered pair (2,20) putting f(2) = 20, we get

$20 = a(b)^{2}$ ............. (2)

Again, for the ordered pair (3,40) putting f(3) = 40, we get

$40 = a(b)^{3}$ ............. (3)

Now, from equations (3) and equation (2) we get,

2 = b

⇒ b = 2.

Now, from equation (2) we get, $20 = a(2)^{2} = 4a$

⇒ a = 5

Therefore, the exponential function will be

$f(x) = 5(2)^{x}$ (Answer)