An article in a medical journal says that a sunscreen with a sun protection factor (SPF) of 2 provides 50% protection against ultraviolet B (UVB) radiation, an SPF of 4 provides 75% protection, and an SPF of 8 provides 87.5% protection (which the article rounds to 87%).

(a) 87.5% protection means that 87.5% of the UVB radiation is screened out. Write as a fraction the amount of radiation that is let in, and then describe how this fraction, in general, relates to the SPF rating.
(b) Plot UVB percent protection (y) against x, where x = 1/SPF.
(c) Based on your graph from part (b), give an equation relating UVB protection to SPF rating.
(d) An SPF of 8 has double the chemical concentration of an SPF 4. Find the increase in the percent protection.
(e) An SPF of 30 has double the chemical concentration of an SPF 15. Find the increase in the percent protection.
(f) Based on your answers from parts (d) and (e), what happens to the increase in the percent protection as the SPF continues to double?