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