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The ordered pairs model an exponential function, where j is the function name and e is the input variable.

{(1, 10),  (2, 50) , ( 3, 250) , (4, 1250)}

What is the function equation in sequence notation?

Respuesta :

siselytrevino24
the answer is 2(5^e)
because 
2(5^1)= 10
2(5^2)=50
2(5^3)=250
2(5^4)=1250
and e is the input variable

Answer:  The answer is [tex]2\times 5^e.[/tex]


Step-by-step explanation:  Given ordered pairs are (1,10), (2,50), (3,250) and (4,1250).

These ordered pairs model an exponential function with function name 'j' and input variable 'e'.

We need to find the equation of the function in sequence notation.

For that, we have to find the similarities among the consecutive terms of the function. Let us start as follows -

The first few terms are

[tex]y_1=10=2\times 5^1=2\times 5^{x_1},\\\\y_2=50=2\times 5^2=2\times 5^{x_2},\\\\y_3=250=2\times 5^3=2\times 5^{x_3},\\\\y_4=1250=2\times 5^4=2\times 5^{x_4},[/tex]

and so on....

Thus, the required exponential function in sequence form is given by

[tex]j=2\times 5^e,[/tex] where e=1, 2, 3, . . . is the input variable.


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