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.

Question

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 range for this context is _________

A.
0 to 110

B.
0 to 750

C.
10 to 70

D.
10 to 1450

E.
750 to 1450

Answer 1

To determine the most reasonable range for the context of Kaylee's savings, we can analyze the function \( m(t) = 70t + 750 \).

Kaylee will be saving for 10 weeks, as stated in the problem. Therefore, \( t \) will vary from 0 (when she starts saving) to 10 (when she finishes saving).

Now let's find the minimum and maximum values of \( m(t) \) over these values of \( t \):

1. When \( t = 0 \): \[ m(0) = 70(0) + 750 = 750 \]

2. When \( t = 10 \): \[ m(10) = 70(10) + 750 = 700 + 750 = 1450 \]

Thus, as Kaylee saves money over the next 10 weeks, her total savings \( m(t) \) will vary from $750 to $1450.

Therefore, the most reasonable range for this context is:

E. 750 to 1450