Web Shooting: A radioactive spider has escaped from the lab and bit you. The spider bite infects (and consequently mutates) 10,0
00 (104 or 1 × 104 ) of your bodies cells. The infection rapidly spreads and number of mutated cells double every 10 minutes. The infection is mutating your Peter Parker cells so that your body remains constant with 50 trillion cells [That’s 5 × 1013!]. (a) Write an equation to express the number of cells Cn that have been infected after n doubling periods. (b) At 5 million (5 × 106 ) cells your spidey senses start to tingle. After how many complete doubling cycles can you hop into your red spandex suit and start fighting crime? (c) At 50 million (5×107 ) cells, your immune system kicks into high gear and kills off 3 4 of the mutated cells every 10 minutes. Write an equation to describe the number of mutated cells present while your immune system combats the infection’s growth. (d) How long until you are no longer able to shoot webs? (Note: You need 5 million mutated cells to start slinging webs.)
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