Answer: The answer is \(2\times 5^e.\)
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
\(y_1=10=2\times 5^1=2\times 5^{x_1},\\\\y_2=50=2\times 5^2=2\times 5^{x_2},\\\\y_3=250=2\times 5^3=2\times 5^{x_3},\\\\y_4=1250=2\times 5^4=2\times 5^{x_4},\)
and so on....
Thus, the required exponential function in sequence form is given by
\(j=2\times 5^e,\) where e=1, 2, 3, . . . is the input variable.
