A new air reshener weighs 26 grams. Once the air reshener is opened, it begins t
ID: 2912042 • Letter: A
Question
A new air reshener weighs 26 grams. Once the air reshener is opened, it begins to evaporate such that the mass of the air res ener decreases by 2.24% each day. Hint: you can enter expressions by typing log-b(a). For example, log 2(4) represents log2(4). gar a. After how many days will the air freshener weigh 8 grams? O days Preview b. After how many days will the air freshener weigh 22 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 mumber of days n that have elapsed since it was opened f(n) = L 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 g(z) =Explanation / Answer
let amount of airfreshner after time n is f(n), rate of decay,r =2.24%=0.0224
equation representing the decay of airfreshner is ,f(n)=26*(1-0.0224)n
a)
airfreshner weigh 8 grams
=>26*(1-0.0224)n=8
=>(1-0.0224)n=(8/26)
=>0.9776n=(4/13)
=>n=log0.9776(4/13) days------------------->answer
=>n=log_0.9776(4/13) days---------------->answer
=>n=52.03 days---------------------------> answer
--------------------------------
b)
=>26*(1-0.0224)n=22
=>(1-0.0224)n=(22/26)
=>0.9776n=(11/13)
=>n=log0.9776(11/13) days------------------->answer
=>n=log_0.9776(11/13) days---------------->answer
=>n=7.37 days---------------------------> answer
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c)
f(n)=26*(1-0.0224)n
f(n)=26 *0.9776n
d)
f(n)= x
=>26 *0.9776n=x
=>0.9776n=(x/26)
=>n=log0.9776(x/26)
=>n=log_0.9776(x/26)
=>g(x)=log_0.9776(x/26)----------------------->answer
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