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The finches on the galapagos island were similar in form except for variations of their beaks. darwin observed that these variations were useful for: attracting a mate defending territory building nests gathering food

Radiometric dating is used to tell the absolute age of materials by studying the decay rate of radioactive isotopes. the decay rates of isotopes are constant and are expressed as .

The kidney filters potentially toxic substances in the blood, and thus “clears” the blood of those substances. this clearance function is dependent upon and proportional to the diffusion gradient of the substance across filtering capillaries, i. e. if the concentration of the substance is doubled, twice as much will be cleared from each ml of blood that is filtered. suppose that the body produces a constant amount of a substance x per unit of time. the kidneys eliminate substance x at a rate directly proportional to the concentration of the substance and the volume of blood cleared each minute (c): elimination = c × [x], where [x] is the steady-state concentration of substance x. imagine an individual with an initial concentration of x equal to [x]0 who develops kidney disease. her baseline clearance c0 drops to one half of the original (½c0). what is the new steady state concentration of x? (for simplicity, assume that substance x is 100% filtered by the kidney).