Question

9. Choose an initial value that is between zero and 4 and is not a whole
number. Iterate it using the function, f, ten times. If necessary, you can
round your results to the nearest ten-thousandth.
10. Choose a second initial value that is 0.01 greater than the initial value from
question 9. Iterate it using the function, f, ten times. If necessary, you can
round your results to the nearest ten-thousandth.

Answer 1

For question 9, let's choose an initial value of 2.5.

First iteration: f(2.5) = 2.5^2 - 2.5 = 4.375
Second iteration: f(4.375) = 4.375^2 - 4.375 = 15.234375
Third iteration: f(15.234375) = 15.234375^2 - 15.234375 = 222.908843994
Fourth iteration: f(222.908844) = 222.908844^2 - 222.908844 = 49488.713559122
Fifth iteration: f(49488.713559) = 49488.713559^2 - 49488.713559 = 2449073327.798126221
Sixth iteration: f(2449073327.7981) = 2449073327.7981^2 - 2449073327.7981 = 6.00097855*10^18
Seventh iteration: f(6.00097855*10^18) = 3.600586131*10^37
Eighth iteration: f(3.600586131*10^37) = 1.296211101*10^75
Ninth iteration: f(1.296211101*10^75) = 1.682599682*10^150
Tenth iteration: f(1.682599682*10^150) = 2.834910296*10^301

Now for question 10, let's choose an initial value of 2.51.

First iteration: f(2.51) = 2.51^2 - 2.51 = 4.4001
Second iteration: f(4.4001) = 4.4001^2 - 4.4001 = 15.36168001
Third iteration: f(15.36168001) = 15.36168001^2 - 15.36168001 = 236.59296451
Fourth iteration: f(236.59296451) = 236.59296451^2 - 236.59296451 = 55881.80372401
Fifth iteration: f(55881.80372401) = 55881.80372401^2 - 55881.80372401 = 3123034473.69517494
Sixth iteration: f(3123034473.6952) = 9.751282633*10^18
Seventh iteration: f(9.751282633*10^18) = 9.508369638*10^37
Eighth iteration: f(9.508369638*10^37) = 9.021162201*10^75
Ninth iteration: f(9.021162201*10^75) = 8.198982932*10^150
Tenth iteration: f(8.198982932*10^150) = 6.723511134*10^301