Final answer:
The rule that represents Eric's age as a function of his sister's age is a(s) = 2(2s) - 2. Eric is 42 years old when his sister is 11.
Step-by-step explanation:
To represent Eric's age as a function of his sister's age, we first need to define the variables. Let s represent the sister's age.
According to the given information, Eric is 2 years younger than 2 times his sister's age. Therefore, we can write the rule as:
a(s) = 2(2s) - 2
To find out Eric's age when his sister is 11, substitute s = 11 into the function:
a(11) = 2(2(11)) - 2
Simplify the expression:
a(11) = 2(22) - 2
a(11) = 44 - 2
a(11) = 42
Therefore, Eric is 42 years old when his sister is 11.