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)}

What is the function equation in sequence notation?

Answer 1

15 * 4^1 = 60
15*4^2 = 240
15*4^3 = 960
15*4^4 = 3840

the function is w = 15(4)^t

Answer 2

Required exponential function is
`w(t)=15(4)^t`

Explanation:

The ordered pairs {(1, 60), (2, 240), (3, 960), (4, 3840)} model an exponential function.

where w is the function name and t is the input variable.

Ordered pair: (t,w)

`\text{Exponential function: }w=ab^t`

`\text{For (1,60) }\rightarrow 60=a\cdot b^1..........(1)`

`\text{For (2,240) }\rightarrow 240=a\cdot b^2..........(2)`

Divide (2) by (1)

`(240)/(60)=(ab^2)/(ab)\Rightarrow 4=b`

Substitute b=4 into eq(1)

60=4a

a=15

Thus, Required exponential function is
`w(t)=15(4)^t`