Aschlen Wags Due Wed 12/06/2017 11 \'ve already done this problem. re on last at

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Aschlen Wags Due Wed 12/06/2017 11 've already done this problem. re on last attempt: 0 out of 1 ore in gradebook: 0 out of 1 eattempt this question uestion with last attempt is displayed for your review only A new air freshener weighs 50 grams. Once the air freshener is opened, it begins to evaporate such that the mass of the air freshener decreases by 2.36% each day. a. After how many days will the air freshener weigh 41 grams? 1.135 days Preview b. After how many days will the air freshener weigh 9 grams? s days Preview c. Define the rule for the function g that determines the number of days that have clapsed in terms of weight of the air freshener, z, in grams. g(z) = # Preview ar 0 2 3 4

Explanation / Answer

Initial = 50 g
Decreass by 2.36% each day

A = A0 * (1 - 2.36%)^t

A = 50(1 - 0.0236)^t

A = 50(0.9764)^t

a)
Now, we need to find t when A = 41 :
41= 50(0.9764)^t

0.9764^t = 0.82

Ln both sides :
t*ln(0.9764) = ln(0.82)

t = ln(0.82)/ln(0.9764)

t = 8.3093176499151733 ---> ANS

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b)
9 = 50(0.9764)^t

9/50 is 0.18
So,
0.18 = (0.9764)^t

So, t = ln(0.18)/ln(0.9764)

t = 71.8 --> ANS

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c)
A = 50(0.9764)^t

x = 50(0.9764)^t

So, x/5o or 0.02x = 0.9764^t

So, t = ln(0.02x)/ln(0.9764)

g(x)= ln(0.02x)/ln(0.9764) ---> ANS

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