Module 2 6 3. The function f(x)- 6.5x2 -204x+234 x2 +36 models the pH level, f(x

Question

Module 2 6 3. The function f(x)- 6.5x2 -204x+234 x2 +36 models the pH level, f(x) of the human mouthx minutes after a person eats food containing sugar a. Determine to the after a person eats food containing sugar. nearest tenth the pH level of the human mouth 42 minutes o O b. What is the equation of the horizontal asymptote assd e ver time associated with this function? Describe what this means in terms of the mouth's pH level over time 4. Suppose a company that manufactures mountain bikes has a fixed monu $100,000 and that it costs $100 to produce each moun a. Write the cost function, C, of producing x mountain bikes. b. Write the average cost function, C, of producing x mountain bikes. C. Find and interpret C (500)E(1,000) , c (2,000) and C (4,000) d. What is the horizontal asymptote for the graph of the average cost function, C? Describe what this represents for the company

Explanation / Answer

4) fixed cost = $ 100,000

$ 100 to produce each bike

So, for producing x no. of bikes

we can write cost function : C(x) = 100,000 + 100x

Average Cost function C_(x) = C(x) = (100,000+10x)/x ---- avg cost per bike

C_(500) = (100,000 +10*500)/500 = 1000/5 + 10 = 200+10 = $ 210 per bike

C_(1000) = (100,000 + 10*1000)/1000 = 10 + 10 = $ 20 per bike

C_(2000) = (100,000 + 10*2000)/2000 = 5 +10 = $ 15 per bike

C_(4000) = (100,000 + 10*4000) /4000 = 2.5 + 10 = $ 12.5 per bike

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