Temperature at noon is 75 degrees. Temperature drops 3 degrees every half hour. What is temperature at 4pm

Question

Need formula to solve

Answer 1

Assume temp T = T₀ (75 ⁰) at Noon (00), To find out T after 4 hours at 4 p.m. or at the 8th period, each period being 0.5 hour. If the relationship is linear, i.e if temperature is dropping linearly each half an hour by 3 ^0, the T is a staight line T=m*t+ T_0, in which the slope m=∇T/∇t = (-3⁰/0.5 hr) = -6⁰/hour (negative slope decreasing)

 

So at 4 p.m.  for t=4, temp T = 75⁰ -6⁰/hour*4 hour= 75⁰-24⁰= 51⁰

 

Temperature at 4 p.m. 51⁰, and equation for temperature at t-th hour is: T=75⁰ - 6⁰/hr* t (hr)

Answer 2

75 degrees minus 3 degrees every half hour

 

=  75 - 8 (3)    there are 8 half hours in 4 hours

 

=  75- 24

 

=  51 degrees