A new air freshener weighs 43 grams Once the air freshener i

A new air freshener weighs 43 grams. Once the air freshener is opened, it begins to evaporate such that the mass of the air ecreases by 4.82% each day. Hint: you can enter logarithmic expressions by typing log b(a). For example, log 2(4) represents log2(4).] a. After how many days will the air freshener weigh 13 grams? days Preview b. After how many days will the air freshener weigh 16 grams? days Preview e. 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 air freshener, d. Define the rule for the function g that determines the number of days that have elapsed in terms of weight of the z, in grams. Preview

Solution

let amount of airfreshner after time n is f(n), rate of decay,r =4.82%=0.0482

equation representing the decay of airfreshner is ,f(n)=43(1-0.0482)ⁿ

a)

airfreshner weigh13 grams

=>43(1-0.0482)ⁿ=13

=>0.9518ⁿ=(13_/43)

=>n=log_0.9518(13_/43) days------------------->answer

=>n=log_0.9518(13_/43) days---------------->answer

=>n=24.21543 days---------------------------> answer

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b)

airfreshner weigh6 grams

=>43(1-0.0482)ⁿ=16

=>0.9518ⁿ=(16_/43)

=>n=log_0.9518(16_/43) days------------------->answer

=>n=log_0.9518(16_/43) days---------------->answer

=>n=20.01 days---------------------------> answer

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c)

f(n)=43(1-0.0482)ⁿ

f(n)=43x0.9518ⁿ

d)

f(n)= x

=>43x0.9518ⁿ=x

=>0.9518ⁿ=(x_/43)

=>n=log_0.9518(x_/43)

=>n=log_0.9518(x_/43)

=>g(x)=log_0.9518(x_/43)----------------------->answer