Kaylee is saving up money to buy a new computer. She already has $750 in her savings account.

Question

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.
Complete the statements.

The most reasonable domain for this context is ____
. The most reasonable range for this context is ____

Answer 1

In this context, Kaylee is saving money over a period of 10 weeks, which provides the timeframe for her savings.

1. Domain: The domain represents the values that \( t \) (the amount of time in weeks) can take. Since Kaylee is saving for 10 weeks, \( t \) can range from 0 weeks (starting point) to 10 weeks (end point). Therefore, the most reasonable domain is: \[ [0, 10] \]

2. Range: The range represents the possible values for \( m(t) \) (the amount of money saved) from the start of her saving up to the end. At \( t = 0 \): \[ m(0) = 70(0) + 750 = 750 \] At \( t = 10 \): \[ m(10) = 70(10) + 750 = 700 + 750 = 1450 \] Therefore, the amount of money saved ranges from $750 to $1450. Thus, the most reasonable range is: \[ [750, 1450] \]

Putting it all together, we have:

• The most reasonable domain for this context is [0, 10].
• The most reasonable range for this context is [750, 1450].