Question

The temperature of a room , y, is based on the number of hours the A/C is on , x. If the temperature is already 74 degrees and it drops/decreases by 3 degrees each hour, write an equation to represent ?​

Part B: What will the temperature be after 4 hours ?

Part C: After how many hours is the temperature 50 degrees ?

Answer 1

Explanation:

If the temperature is already 74 degrees and it drops/decreases by 3 degrees each hour, it means that the temperature I'd decreasing in an arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 74 degrees

d = - 3 degrees (it is decreasing)

Tn = temperature after n hours.

The equation becomes

Tn = 74 - 3(n - 1)

Part B

The temperature after 4 hours would be T4

T4 = 74 - 3(4 - 1) = 74 - 3 × 3

T4 = 65 degrees

Part C

50 = 74 - 3(n - 1)

50 = 74 - 3n + 3

3n = 74 + 3 - 50 = 27

n = 27/3 = 9 hours