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I got stumped on a problem from an Intermediate Algebra classrelated to exponent

ID: 3092553 • Letter: I

Question

I got stumped on a problem from an Intermediate Algebra classrelated to exponential growth and decay. How would you solve thefollowing problem?

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The National Marine Fisheries Service research concluded that thepopulation of sockeye salmon in Lake Ozette (Olympic Peninsula)declined from about 1000 in '77 to about 600 in '97. Let "t" be thenumber of years since '77 and create and exponential model for thepopulation decline in the form of P(t)_______(________)t.

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Explanation / Answer

P(t) = P0e-rt Find r: P(20) = 600 => 1000e-r(20) = 600 => e-r(20) = 600 / 1000 = 0.6 => ln e-r(20) = ln 0.6 => -r(20) ln e = ln 0.6 => -r(20) = ln 0.6 => r = ( ln 0.6 ) / - 20 = 0.0255412812 ˜ 0.0255 => P(t) = 1000e-0.0255t Check: P(20) = 1000e-0.0255(20) = 600.495579 ˜ 600