A new air freshener weighs 34 grams. Once the air freshener is opened, it begins

Question

A new air freshener weighs 34 grams. Once the air freshener is opened, it begins to evaporate such that the mass of the air freshener decreases by 3.54% each day. log b(a). For example, log 2(4) represents log2(4).3 Hi a. After how many days will the air freshener weigh 3 grams? days Preview b. After how many days will the air freshener weigh 32 grams? days Preview c. Define the rule for the function f that determines the weight of the air freshener in grams in terms of the number of days n that have elapsed since it was opened f(n) = Preview d. Define the rule for the function g that determines the number of days that have elapsed in terms of weight of the air freshener, z, in grams. Preview Points possible: 10 Unlimited attempts. Score on last attempt:O.Score in gradebook: 0 Post this question to forum Submit

Explanation / Answer

a) the new air freshener weighs 34 grams

decreases at 3.54% each day

a) so we can write the equation as

A(t) = 34 e^-.0354 t

airfreshener weighs 3 grams

3 = 34 e^ -.0354 t

3/34 = e^-.0354 t

t = 68.58 days

b) 32 = 34 e^ -.0354 t

32 / 34 = e^-.0354 t

t = 1.713 days

c) f(n) = 34 e^ -.0354 n

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