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Precalculus Mathematics Homework Help
Finding constants in exponential functions
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[QUOTE="LivvyS, post: 4982441, member: 538300"] [h2]Homework Statement [/h2] In 2000 the population of a country was estimated to be 8.23 million. In 2010 the population was 9.77 million. Assume that the number of people P(t) in millions at time t (in years since 2000) is modeled by the exponential growth function. P(t) = Ae[SUP]kt[/SUP] Find P(t) giving the two constants in it to 2 significant figures. [h2]Homework Equations[/h2] P(t) = Ae[SUP]kt[/SUP] [h2]The Attempt at a Solution[/h2] P(0) = 8.23x10[SUP]6[/SUP] so Ae[SUP]0k[/SUP]= 8.23x10[SUP]6[/SUP] P(10) = 9.77x10[SUP]6[/SUP] so Ae[SUP]10k[/SUP]= 9.77x10[SUP]6[/SUP]Divide to eliminate A: Ae[SUP]0k[/SUP]= 8.23x10[SUP]6[/SUP] / Ae[SUP]10k[/SUP]= 9.77x10[SUP]6[/SUP] = e[SUP]0k-10k[/SUP]= 8.23x10[SUP]6[/SUP] / 9.77x10[SUP]6[/SUP] = e[SUP]-10 k[/SUP] = 8.23x10[SUP]6[/SUP] / 9.77x10[SUP]6[/SUP] (I am not certain that this step is right) -10k = ln 8.23x10[SUP]6[/SUP] / 9.77x10[SUP]6[/SUP] k = 0.01917945693 To find A: Ae[SUP]10k[/SUP]= 9.77x10[SUP]6[/SUP] Ae[SUP]10*0.01917945693[/SUP]= 9.77x10[SUP]6[/SUP] A = 9.77x10[SUP]6[/SUP] / e[SUP]10*0.01917945693[/SUP] = 8064904.714 These values for k and A seem to produce 9.77x10[SUP]6[/SUP] when 10 (years) is plugged into the function, however I can't seem to produce 8.23x10[SUP]6[/SUP] at 0 years since 2000 and I can't seem to see why, any help would be much appreciated! [/QUOTE]
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Precalculus Mathematics Homework Help
Finding constants in exponential functions
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