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## Homework Statement

## Homework Equations

no equations required

3. The Attempt at a Solution

3. The Attempt at a Solution

**a)**

__so for part c) i came up with two formula's for the tortoise series:__

the first formula (for the toroise series) is Sn = 20n This formula makes sense and agrees with part a). for example, if the time in minutes is 4, then the distance the tortoise travels will be Sn = 20(4) = 80 m

I came up with another formula for the tortoise series, but im not sure if this one is correct. I was following my lesson when i came up with the formula:

__I came up with a formula for the Hare series:__

__can you please tell me which formula is the right one for the tortoise series, and also if I did the hare series formula correctly?__

*For part d) of question 60, I was asked to graph each function. But im not sure what to graph, do I graph the formula's that were made in part c), or do i use the specific points from part a) and b)???

*I am aware that I am supposed to use the graphs created in part d) to answer part e). Part e) requires me to analyze the graphs and determine who wins the race, either the tortoise or hare. However, just by using the formula's, I can determine who wins. Does the following explanation make sense??

for the tortoise, the formula is Sn = 20n

I have to determine the amount of time it will take the tortoise to complete the race, so i can substitute 2000 m in replace of Sn and solve for the variable n.

2000 = 20n

2000/20 = n

100 = n

it will take exactly 100 minutes for the tortoise to complete the race.

for the hare, the formual is

i can substitue 100 minutes in replace of the variable n in the above formula for the hare, to determine the movement of the hare during the hundredth minute.

Sn = (1000)(1-0.5^100) /0.5

Sn =0.000000000000000000000000000789 meters = 0 meters

so after 100 minutes, the hare hasn't actually reached the finish line. At the hundredth minute, the tortoise passes the finish line, while the hare is moving closer to it. This means that the tortoise wins the race. I read online that in this specific problem, the hare would never actually reach the finish line (theoretically speaking).

are my answers correct?

also, please advise me on what to do for part c), d), and e)

thankyou for all the help! :D