Question
how long does it take an ant to build a tunnel?
duc ok Math 241 Project 1: Ant Tunnel Building Directions: Work on this project in groups of two to four students total. Everyone in the class must work with one or more peers - this is not intended to be an individual assign- ment! If you are able to fit all of your work and explanations onto this sheet, you may turn it in without further supporting papers. Attach other pages as nec and submit the full packet by the deadline submit one paper together rather than several individual reports. ted on Moodle. Your group may Project Statement How long does it take an ant to build a tunnel? If you ever had an ant colony, you may have some intuition on the answer to this question based off of watching the ants working industriously. To begin to answer the question, we need to narrow the scope of the problem, simplify it, and identify some terms and variables before we can proceed to a solution. Let g be the length of the tunnel, in feet, that the ant builds. Let Ta) be the time in hours it takes the ant to build the tunnel of length We can get some idea of the situation by considering the following (rough) sketch nd (slightly better) figure: (a) Crude sketch for ant tunnel building model. Tunnel (b) Useful diagram for discovering the time it takes to build a small section of the ant tunnel from distance r tor + h. Tunnel
Explanation / Answer
2) T(x+h) is not equal to T(x)+T(h) , because T(x+h) denotes the same continous tunnel whiLE t9x) and T(h) may be separely diffrent tunnels.
3) a) reject, because at h = 0,equation may give values other than 0
b) reject, because at h = 0 equation give value 1 in the place of 0
c) reject, because at x = 0 equation give 0 time for make h distance tunnel
d) rejected, because for diffrent value of h we gat the same answer,which is not currect
4) a) equation may be T(x+h) - T(x) = h/v
where v is the constant rate in feet/hour at which ant is making the tunnel
b) dt ( T(x+h) - T(x) ) = h/dx
