Question

33. A scientist is measuring the temperature change in a chemical compound. The temperature dropped 11°F per hour from the original temperature. After four hours, the temperature was 90°F. Find the compound's original temperature.

34. A mountain climber ascend 800 feet per hour from his original position. After six hours, his final position is 11,600 feet above sea level. Find the climbers original position.

Answer 1

33.
134 degrees. You just multiply the change per hour (11) by the amount of hours (4) and add that to the temp after 4 hours (90) and 44+90=134.

34.
6,800 ft. above sea level. Pretty much same explanation as above.

Answer 2

Explanation:

Given that temperature dropped 11 degree per hour

Rate of change of temperature with respect to one hour = -11

Let T be temp and t be time in hours.

Since rate of change is constant we have linear relation

`T=-11t+C`, where C is temperature when t =0

Given that

`T(4) = -11(4)+C=90\\C =134\\`

So original temperature = C =134

34) Slope = 800

Hence if h is the height and t is time in hour,

`h=800t+C` where C is the original height

`h(6) = 800(6)+C =11600\\C = 6800`

Original position = 6800 feet.