The problem is: when a sunscreen lotion of SPF 30, is applied in a layer of only 5μm instead of the calibration layer of 20 μm, 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 μm, as the depth in the suncream layer. x=0 is at the top side exposed to the sun, and x=20μm (or x=5μm ) is on the skin side of the suncream layer.

The intensity of the UV light is I(x), and I(0)=Ifull, 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).