in 2009 there was an endangered population of 270 cranes in a western state. Due to wildlife efforts, the population is increasing at a rate of 5% per year. a. What exponential function would be a good model for this population of cranes? b. If this trend continues, how many cranes will there be in this population in 2020?

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assuming compount interest format [latex]A=P(r+1)^t[/latex] for compounded per 1 year A=future amount P=present amount r=rate in decimal t=time in years given P=270 r=5%=0.05 the equaton is [latex]A=270(0.05+1)^t[/latex] or [latex]A=270(1.05)^t[/latex] for any year, 2009, is year 0, so if you wanted to input the year then [latex]A=270(1.05)^{t-2009}[/latex] would be for t=what year it was A. [latex]f(x)=270(1.05)^t[/latex] b. 2009 to 2020 2020-2009=11 years t=11 [latex]f(11)=270(1.05)^{11}[/latex] f(11)=461.792 about 462 cranes A. [latex]f(x)=270(1.05)^t[/latex] B. about 462

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