Question

100 points

Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) = 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x − 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done. (10 points)

Answer 1

Explanation:

Arthur can create a combined function, let's call it C(x), to represent the total amount of money he has after x weeks. The combined function is the sum of the money in the piggy bank (s(x)) and the money he earns from doing laundry (a(x)).

C(x)=s(x)+a(x)

Given that s(x)=85 and a(x)=10(x−1), substitute these into the equation:

C(x)=85+10(x−1)

Now, simplify the expression:

C(x)=85+10x−10

Combine like terms:

C(x)=10x+75

So, the combined function 10x+75, represents the total amount of money Arthur has after x weeks, considering both the money in the piggy bank and the allowance from doing laundry.