Problema Solution

When a fair skinned person visits “I Want a Tan Tanning Salon” they are advised to

start with 10 minutes of exposure and gradually build up to a maximum of 22

minutes of exposure, increasing exposure 1 minute every 2 days. Write an

equation to determine the minutes of exposure a fair person can experience after n

days. How many minutes could be experienced after 1 week? Two weeks? A

month?

Answer provided by our tutors

let f(x) be the function that describes the minutes if exposure after x days


they are advised to start with 10 minutes thus


f(0) = 10


increasing exposure 1 minute every 2 days thus


f(2) = 10 + (2/2)*1


f(x) = 10 + (x/2), if x is even

f(x) = 10 + (x-1)/2, if x is odd


and since f max = 22 min and it is achieved after m days that is


f(m) = 10 + m/2


10 + m/2 = 22


m/2 = 12


m = 24 days


The equation to determine the minutes of exposure is


f(x) = 10 + (x/2), if x is even, x <= 24

f(x) = 10 + (x-1)/2, if x is odd, x<= 24

f(x) = 22, if x > 24


How many minutes could be experienced after 1 week?


since 1 week = 7 days


f(7) = 10 + (7 - 1)/2 = 13 minutes


Two weeks = 14 days


f(14) = 10 +14/2 = 17 minutes


A month = 30 days > 24


f(30) = 22 min