Question

Please please help!
An air freshener starts with 44 grams and evaporates. In each of the following cases, write a formula for the quantity, Q grams, of air freshener remaining t days after the start.

(a) The decrease is 4 grams per day.
Q(t) =

(b) The decrease is 9% per day.
Q(t) =

(c) The decrease is at a continuous rate of 12% per day.
Q(t) =

Answer 1

well i'd guess,
(a) Q(t) = 4(11-t) // since at day 1 it would be 4(10) = 40 , day 2 = 4(9) = 36 ... etc

(b) Q(t) = 44( 91%^t )
// since Day 1 = 44 *91% , Day 2 = (44 * 91%) * 91% ... etc

(c) Q(t) = 44 - (12%) * t
// since i assumed that by "continuous" the problem meant that the decrease is constant to the original. I could be wrong though, I hope someone could double-check me or something.
well that's what i thought of, I hope you can find your solution if this isn't it.

Answer 2

(a) The decrease is 4 grams per day.
In t days, 4 * t grams would have been lost.
What is left is Q(t) = 44 - 4t = 4(11 - t)

(b) The decrease is 9% per day.
Use the "compound interest formula": Q(t) = 44( 1- 0.09)^t = 44(0.91)^t

(c) The decrease is at a continuous rate of 12% per day.
Every INSTANT it is decreasing not just at the end of each day.
Use the "continuous compounding formula": Q(t) = 44e^(.12t)

Answer 3

the first and second are right the third shows it's wrong

Answer 4

well i figured my interpretation was pretty shaky, thus i asked for a double-check.

Answer 5

c) \(\large Q(t) = 44e^{-0.12t}\)