Question

The ordered pairs model an exponential function, where w is the function name and t is the input variable. {(1, 60), (2, 240), (3, 960), (4, 3840)}{(1, 60), (2, 240), (3, 960), (4, 3840)} What is the function equation in sequence notation? Enter your answer in the box.

Answer 1

Hello there.

The ordered pairs model an exponential function, where w is the function name and t is the input variable. {(1, 60), (2, 240), (3, 960), (4, 3840)}{(1, 60), (2, 240), (3, 960), (4, 3840)} What is the function equation in sequence notation? Enter your answer in the box.

w = 15 (4^t)

Answer 2

We are given the set of points
{(1, 60), (2, 240), (3, 960), (4, 3840)}{(1, 60), (2, 240), (3, 960), (4, 3840)}
If w is the function name and t is the input variable, then the equation has the form
w = k a^t
Plugging in any two of the points to solve for k and a
Choosing (1, 60) and (2, 240)
60 = k a
k = 60 / a

240 = k a^2

Substituting
240 = 60/a (a^2)
a = 4
and
k = 60 / 4 = 15

The function is
w = 15 (4^t)