LostSeaPage2.page

PROBLEM #3: Distance = (rate)(time) (Submitted by Marisa and Dima)
A. The 1.5 mile walking tour of the Lost Sea Cave, including 30 minutes of rest and observation time and a 15-minute boat ride, takes an average of 1 hour and 45 minutes. Find the rate of actual walking travel through the cave. _____________________________
B. If a tour of 50 tourists can begin the guided tour through the cave every 20 minutes, find the maximum number of tourists that could tour the cave on a summer Sunday when the cave is open 9 a.m. until 7 p.m. (Keep in mind that the last tour must begin 1 hour and 45 minutes prior to closing time. ___
C. The trail slopes slightly. If the slope of the very steepest part of the walkway through the Lost Sea Cave trail drops 2 feet for every 10 feet of walking trail, find the per cent grade of the steepest part of the trail. ___________________

Josh admiring stalactites in the Lost Sea Remains of a Moonshine still
found in the cave

PROBLEM #4: (Circular Area)                                                                   (Submitted by Josh)
The Cherokee Council Room at the Lost Sea was so named because of the numerous coals and charcoal remains found in the nearly circular area with a natural seating arrangement carved into the cave formations.
A. If the diameter of the room measures approximately 55 feet, find the total area of the circular council room. ___________________
B. If a person occupies approximately 3 square feet of standing area, what would have been the absolute maximum number of Cherokees meeting in the council room at a given time? ____________

PROBLEM #5:   (Carbon Dating)                                                               (Submitted by Allison)
The earliest date found inscribed on the walls of the Lost Sea Cave was carbon dated in 1974 and found to be accurate. Use the carbon dating formula to find the actual graffiti date found in the cave.
____________________

           R = [10^(-12)]x e^(t/k), R = ratio of carbon in the quantity in 1974 = 10^(-14)
                                               t = time measured in years
                                               k = constant of decay for carbon in the cave wall = -24.1033

Cave graffitti and magnificent stalactites.

ANSWERS TO LOST SEA PROBLEMS
1. A. 1:100 = 36:a, age ~ 3,600 years;       B. 1 mm:1year = 3048mm: a, age ~ 3,048 years
2. 60:p = 3:75, population ~ 1500 fish
3. A. rate = (1.5)(1 hour) = 1.5 mph        B. 50(24 tours) = 1500 people        C. 2/10 = 20 %
4. A. area = (3.1416)(55/2)^2 ~ 2375.83 square feet             B. 2375.83/3 ~ 791 people
5. t = -24.1033(-2)(ln10) ~ 111 years, 1974 -111 = 1863, the inscribed date (See photo below)