Problem1: Let N=f(H) give the number of days it takes a certain kind of insect t

Question

Problem1:

Let N=f(H) give the number of days it takes a certain kind of insect to develop as a function of the temperature H (in C?). At 35?C—the maximum it can tolerate—the insect requires 20 full days to develop. An additional day is required for every 2?C drop, and it cannot develop in temperatures below 5?C.

Problem2: Tuition cost T, in dollars, for part-time students at a college is given by T=400+250C, where C represents the number of credits taken. Part-time students have to take at least one credit hour and cannot take more than 11 credit hours. Give a reasonable domain and range for this function.

Give the domain and range of the function described. Let N-f (H) give the number of days it takes a certain kind f insect to develop as a function of the temperature H (in C). At 35 C-the maximum it can tolerate-the insect requires 20 full days to develop. An additional day is required for every 2 C drop, and it cannot develop in temperatures below 5°C. The domain is [5 The range is 20... H35 35

Explanation / Answer

We have N =f(H) where H is the temperature in 0C nd N is the number of days that a certain kind of insect takes to develop. The insect cannot develop in a temperature below 50 C and above 350C. Hence the domain of the function N =f(H) is the viable values of H i.e. [5,35] or, 5 H 35. Further, the minimum time that the insect takes to develop is 20 days(at a temperature of 350 C and the time taken by the insect to develop increases by 1 day for every 20 C drop. Now, since (35 -5)/2 =30/2 = 15, hence the insect will take 20+15 = 35 days, if the temperature drops to 50 C. Hence the range of the function N =f(H) is [ 20,35] or, 20 N 35. The Tuition cost T, in dollars, for part-time students at a college is given by T=400+250C, where C represents the number of credits taken. Part-time students have to take at least one credit hour and cannot take more than 11 credit hours. When C = 1, T = 400+250 = 650 and when C= 11, T = 400+250*11 = 400+2750 = 3150. The domain of the function is the interval between its minimum and maximum values i.e. [1,11] or, 1 C 11. Also, the range of the function is the interval to which T belongs i.e. [ 650, 3150] or, 650 T 3150.

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