ry Bookmarks People Window Help 04 4 Wed 1039AM Daniel Kaliu

ry Bookmarks People Window Help 04: ,4%\"> Wed 10:39AM Daniel Kaliush Q, à https://imathas.ratio .net/ showtest.php?ac 7&reattempt; 111-02-Berghout-F16 > Assessment nv 9 Daniel Kallu Due in 23 burs, 30 minutes. Due Tha llia2016 10:00 Shov Imro/lestrction er weighs 31 grams. Once the air freshener is opened, it begins to evaporate such that the mass of the air treshener decreases by 3,.13% cach day.(Hint you can ener A new air freshener weighs 31 grams. Once the air freshener is logarithmic expressions by typing log be). For example, log 214) represents kog (4)1 /10] i0] 10j /10) 10) 10] 10] 10 0) 10) a After how many days will the air freshener weigh 26 grams? . days Preview b. After how many days will the air freshener weigh 16 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 clapsed since it was opened. (n)-museeern Preview . 0 number of days that bave elapsed in terms of weight of the air freshener, z, in grams d. Define the rule for the function g that determines the number of days that have elapsed in terms of weight of the air Preview g(z)-busta 11 Points possible: 10 Unlimited attempts Score on last attempt: 0. Score in gradebook: 0 Message instructor about this question Post this question to forum Submit Show A 40.drng

Solution

fresher decreases by 3.13%

f(n) = 31(1 -r)^n = 31(1 - 0.0313)^n

f(n) = 31(0.9687)^n

a) f(n) = 26 ;

26 = 31(0.9687)^n

26/31 = (0.9687)^n

take natural log on both sides:

ln(0.838) = n*ln(0.9687)

n = ln(0.838)/ln(0.9687)

n = ln_0.9687(0.838)

b) f(n) = 16 gms

16 = 31(0.9687)^n

ln(0.516) = n*ln(0.9687)

n = ln_0.516(0.9687)

c) f(n) = 31(0.9687)^n

d) So, f(n) =x

x = 31(0.9687)^n

(x/31) = 0.9687)^n

take log on both sides:

ln(x/31) = n*ln(0.9687)

n = ln_0.9687(x/31)