1.5 Mathematical model

Course subject(s) 1. Introducing Mathematical Modelling

The problem is: when a sunscreen lotion of SPF 30, is applied in a layer of only 5 $μ$ m instead of the calibration layer of 20 $μ$ m, how long can children stay out in the sun, when their skin would start to redden after 10 minutes without suncream?

Define the independent variable $x$ in $μ$ m, as the depth in the suncream layer. $x = 0$ is at the top side exposed to the sun, and $x = 20 μ$ m (or $x = 5 μ$ m ) is on the skin side of the suncream layer.

The intensity of the UV light is $I (x)$ , and $I (0) = I_{f u l l}$ , the intensity that is such that unprotected, light skinned children can tolerate 10 minutes of it midday on a summers day.

In the next section, you will solve this differential equation for $I (x)$ : you will integrate the differential equation for $I (x)$ .

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