Kaylee is saving up money to buy a new computer. She already has 750

Question

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.

Complete the statements.
The most reasonable domain for this context is
. The most reasonable range for this context is

Answer 1

To analyze the problem context, we're working with a function where \( m(t) = 70t + 750 \).

Domain:

• The domain represents the amount of time (in weeks) that Kaylee has been saving.
• Since she will save for the next 10 weeks, the time \( t \) will start at 0 (the current time) and go up to 10 (the end of the 10 weeks).
• Therefore, the most reasonable domain for this context is \( [0, 10] \) (meaning she can save for any time \( t \) from week 0 to week 10).

Range:

• The range represents the total amount of money saved by Kaylee after \( t \) weeks.
• At \( t = 0 \): \[ m(0) = 70(0) + 750 = 750 \]
• At \( t = 10 \): \[ m(10) = 70(10) + 750 = 700 + 750 = 1450 \]
• Therefore, the range of the function, which includes all possible total amounts saved from week 0 to week 10, is from the amount she starts with to the amount she will have after saving for 10 weeks.
• Thus, the most reasonable range for this context is \( [750, 1450] \).

In summary:

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