Answer:
Required exponential function is [tex]w(t)=15(4)^t[/tex]
Step-by-step 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)
[tex]\text{Exponential function: }w=ab^t[/tex]
[tex]\text{For (1,60) }\rightarrow 60=a\cdot b^1..........(1)[/tex]
[tex]\text{For (2,240) }\rightarrow 240=a\cdot b^2..........(2)[/tex]
Divide (2) by (1)
[tex]\dfrac{240}{60}=\dfrac{ab^2}{ab}\Rightarrow 4=b[/tex]
Substitute b=4 into eq(1)
60=4a
a=15
Thus, Required exponential function is [tex]w(t)=15(4)^t[/tex]
