Chapter 7.5, Problem 47MS

More prediction peril. Consider the previous Mindscape but now use the model: $P_{n+1}=P_n+1.3(1-P_n).$

This time, if $P_1=0.2,$ then $P_2=0.2+1.3(1-0.2)=0.2+1.3(0.8)=0.2+1.04=\mathrm{1.24.}$ So with a much larger coefficient (1.3 instead of 0.3), the model predicts a much greater increase in population density from Year 1 to Year 2. hat does the model predict for Year 3? For Year 4?