Question

(4) You are hiking a trail. Your elevation (in thousands of feet above sea level) is given by d(t) where t is in hours since the start of the hike (a) Interpret d(5) = 1. Include units. 5JAsur uAn de have ben hikng fe 5 hows, na hw ot hkag 2)d)out ut KAs eva (a Mansad of k) elevasn fy h Shpu (esu (4 in an tacrtase in elevasjon of abent one honsa fees above sa level. Thou (b) Interpret (dY(5) = 0.7. Include units (e) Given that d'(4)< 0. Which of the following must be TRUE? Circle all that apply (i) Before the start of your hike, your elevation is 4,000 feet (i When you are 4 hours into your hike, you are below sea level (ii) When you are 4 hours into your hike, your elevation is decreasing. (iv) When you are 4 hours into your hike, your rate of change of elevation is decreasing

Answer 1

(A)                Given d(t) = e . where t is the time elapsed since the start of the hike.

      So the inverse will be (e) = t.. it says the t is time taken to go reach "e" level of elevation.

       Therefore , in the given question i.e, (5) = 1 says it takes 1 hour to reach 5 thousand feet of elevation above sea level.

(B)               Lets look at the expression
d 1Y
(e) .. Since (e) says the time taken to reach "e" level

      Its differentiation will say the rate of change of time at that level of elevation..

   Therefore,in the given question i.e, (5) = 0.7 says the rate of change of time at 5 thousand feet of elevation is 0.7 hours per feet.

d 1Y

(C) Similarly , since d(t) = e gives the elevation 'e' after t hours of hiking. (t) says the rate of change of elevation at time t hours after the start of hike.

Therefore, the given expression (4) < 0 means the rate of change of elevation is negative (doesn't necessarily mean decreasing). Since the rate at which the elevation changes is negative , this implies that elevation will decrease from now.. But it doesnt give any information about starting elevation or the elevation itself.

Only option (iii) is correct.