58+ 40t +2t Suppose the number of employees of a start-up company is given by t0

Question

58+ 40t +2t Suppose the number of employees of a start-up company is given by t0) where t is the number of months after the company is organized Complete parts (a) and (b) below a. For what values of t is 1(0)s 187 Solve the inequality for t. Select the correct choice below and fill in any answer boxes to complete your choice O A. The solutions are the values of t in the interval O B. The solution(s) is/are t O C. There is no solution b. During what months is the number of employees below 18 The number of employees is below 18 during the frst month Type your answer in interval notation) (Use a comma to separate answers as needed

Explanation / Answer

f = (58 + 40t) / (7 + 2t)

(58 + 40t)/(7 + 2t) - 18 <= 0

(58 + 40t - 18(7 + 2t)) / (7 +2t)) <= 0

(4t - 68)/(7 + 2t) <= 0

Key values are :
4t - 68 --> t = 17
7 + 2t = 0 --> t = -3.5

So,
region 1 : (-inf , -3.5)
Test = -4
We find (4t - 68)/(7 + 2t) to be > 0

Region 2 : (-3.5 , 17)
Test = 0
We find (4t - 68)/(7 + 2t) < 0 as needed

Region 3 : (17 , inf)
Test = 18
Doesnt work as it is (4t - 68)/(7 + 2t) > 0

So, we need <= 0

So, (-3.5 , 17)

Now, we cannot plug in t = -3.5 cuz this'll render denominator = 0, aint happenin'!

Now, with t = 17, num = 0
and this is possible cuz we had <= 0

So,
(-3.5 , 17] ------> ANS

Didnt work?

Plz try [0 , 17]

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b) 17 months ---> ANS

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