I've formed a difference equation to calculate the rate of change in a population of weasels, which I then solved to find tan expression for the population at time $n$. The expression I got was $y(n)=-4450(1.05)^{n}+240n+4800$. How would you find the value of $n$ for which $y(n)=0$?
2025-01-13 00:02:46.1736726566
How would you solve the equation $-4450(1.05)^{n}+240n+4800=0$?
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This is a non-linear equation which cannot be solved algebraically (unless you "know" about LabertW functions).
Usually this sort of equation is solved numerically (i.e. find an approximate solution) by software (either a graphing calculator or some sort of mathematical software like Maple, Mathematica, etc).
Wolfram alpha provides a free online route to a solution.
Alpha says that $n \approx 9.55784$ is a solution.
Maple: