Kaylee is saving up money to buy a new computer. She already has $750 in her savings account. She needs to save $70 for the next 10 weeks from her weekly paycheck to have enough money to buy the computer.

This context is modeled by the function m(t)=70t+750, where m represents the amount of money saved and t represents the amount of time (in weeks) Kaylee has been saving.

The most reasonable domain for this context is _________
A. 0 to 110
B. 0 to 750
C. 10 to 70
D. 10 to 1450
E. 750 to 1450

1 answer

The function \( m(t) = 70t + 750 \) represents the amount of money Kaylee has saved after \( t \) weeks. Given that she plans to save for 10 weeks, the most appropriate domain for \( t \) (the time in weeks) is from 0 to 10.

Thus, the most reasonable domain for this context is:

A. 0 to 10

However, since "0 to 10" is not listed in your options, we should interpret the total amount she will have saved after those 10 weeks, which will be:

\[ m(10) = 70 \cdot 10 + 750 = 700 + 750 = 1450 \]

So in terms of the amount of money saved, after 10 weeks, she will have saved between her initial amount of $750 and the final amount of $1450, which is why we evaluate based on the amounts given.

However, from the options:

  • A. 0 to 110
  • B. 0 to 750
  • C. 10 to 70
  • D. 10 to 1450
  • E. 750 to 1450

D. 10 to 1450 seems to be the closest match for the context provided, because it signifies the progression from the saving period (10 weeks) to the total amount saved.

Given these options and the context, D. 10 to 1450 would be the most suitable.