Question
The amount of toilet paper in a grocery store’s inventory decreases at a rate of 2% per week. The amount of paper in a store was originally 659 rolls.
Which function models the amount of toilet paper left in this store after w weeks?
Responses
A f(w) = 659(1.02)wf ( w ) = 659(1.02) w
B f(w) = 0.98(659)wf ( w ) = 0.98(659) w
C f(w) = 659(0.98)wf ( w ) = 659(0.98) w
D f(w) = 1.02(659)w
Which function models the amount of toilet paper left in this store after w weeks?
Responses
A f(w) = 659(1.02)wf ( w ) = 659(1.02) w
B f(w) = 0.98(659)wf ( w ) = 0.98(659) w
C f(w) = 659(0.98)wf ( w ) = 659(0.98) w
D f(w) = 1.02(659)w
Answers
Answered by
GPT-4o mini
To model the amount of toilet paper left after a certain number of weeks when it decreases at a rate of 2% per week, we need to use a decay function.
- Starting amount of toilet paper: 659 rolls
- Decrease rate: 2% means that 98% of the paper remains after each week.
A 2% decrease means that after each week, you multiply the current amount by (1 - 0.02) = 0.98. So after \( w \) weeks, the amount of toilet paper left can be modeled by the function:
\[
f(w) = 659 \times (0.98)^w
\]
Thus, the correct response is:
C: \( f(w) = 659(0.98)^w \)
- Starting amount of toilet paper: 659 rolls
- Decrease rate: 2% means that 98% of the paper remains after each week.
A 2% decrease means that after each week, you multiply the current amount by (1 - 0.02) = 0.98. So after \( w \) weeks, the amount of toilet paper left can be modeled by the function:
\[
f(w) = 659 \times (0.98)^w
\]
Thus, the correct response is:
C: \( f(w) = 659(0.98)^w \)