Problem $4$: Hailstone Sequences

In mathematics, a hailstone sequence is a sequence creates as follows:

$$ Select a starting value for the sequence.

$$ If a particular term in the sequence is equal to $,$ then the next term will be equal to $/2$ if $$ is even, and will be

equal to $3+1$ if $$ is odd.

$$ The sequence continues until reaching a term that is equal to $1.$

For example, the hailstone sequence beginning with $12$ is: $12,6,3,10,5,16,8,4,2,1$

It is widely believed that any starting value will result in a sequence that eventually reaches $1,$ but this has not been proven

to be true.

Use while loops to calculate the hailstone sequences beginning with $15,17,$ and $22,$ storing the sequences $($in order$)$ in

lists named hs$15,$ hs$17,$ and hs$22.$ This will require three separate $($but nearly identical$)$ loops. The elements stored in

the lists should be integers $($as opposed to floats$).$ Print the contents of the three lists.

Problem $5$: Predator$/$Prey Model

Assume that a certain ecosystem contains both rabbits and wolves. The size of the rabbit population and the size of the

wolf population both fluctuate, and have an effect on each other. Suppose that the current sizes of the populations can be

used to determine the sizes of the populations one year from now according to the following population model:

$$ Let A be the current size of the rabbit population.

$$ Let B be the current size of the wolf population.

$$ Let C be the size of the rabbit population one year from now.

$$ Let D be the size of the wolf population one year from now

$$ The population sizes one year from now are determine by the following equations:

C$=1\mathrm{.}5$ A $0\mathrm{.}002$ A $$ B

D $=0\mathrm{.}8$ B $+0\mathrm{.}0003$ A $$ B

Suppose that the current rabbit population is $1000$ and the current wolf population is $200.$ Under these circumstances, the

populations will fluctuate for several years, but the rabbit population will eventually die out completely.

In this problem, you will be asked to calculate the size of each population at the end of each year until the the rabbit

population dies out.

Perform the following steps in a single code cell:

$1.$ Create variables r$\_$pop and w$\_$pop to store the current rabbit and wolf populations $($which are provided above$).$

$2.$ Print the first three rows of the table shown below $($the column headers, the dashed line, and the year $0$ info$).$

$3.$ Use a loop to determine the new populations at the end of each new year. Each time the loop executes,

perform the steps below. The loop should continue to run for as long as both populations are greater than zero.

$$ Store the current population values in temporary variables named r$\_$pop$\_$prev and w$\_$pop$\_$prev.

$$ Use the formulas provided to calculate the new population sizes. Round the results to the nearest

integer, and store these values in r$\_$pop and w$\_$pop $($as integers$).$

$$ If any population end up being negative, it should be changed to $0.$

$$ Print a new line of the table below with updated values.

Year r$\_$pop w$\_$pop

$-----------------------$

$01000200$

$11100220$

$21166249$

$.........$

No lists should be created for this problem, and only one loop should be used.