Two Questions PLEASE HELP WITH BOTH Question 1 The cost of b

Two Questions: PLEASE HELP WITH BOTH!

Question 1. The cost of building the toll road is $10,000,000 plus a 30% profit for the construction company. The City of Cedar Springs is willing to donate $2,000,000 to the project. Therefore, the total cost for the toll road that must be covered by the drivers in Cedar Springs is $11,000,000. The fee will be determined by dividing the total cost by the number of users.

1. Write a function that gives the fee in terms of the number of users. Identify your variables and use your graphing calculator or graph paper to graph the function.

2. Determine the domain and range of the function.

3. Explain the difference between the domain and range of the function and the reasonable domain and range of the problem situation. Justify your answer.

4. Write the equations of the asymptotes?

5. Explain the meaning of the asymptotes in terms of the problem situation.

Question 2. In Unit 6 you solved a problem in which three students in the high school Ecology Club suggested exponential models for annual human use of the Oakridge Tract recreational area.

y₁ = 1000(1.20)^x, y₂ = 1000(1.30)^x and y₃ = 1500(1.20)^x, where x is the number of years since the initial population estimates were made andy is the number of people using the recreational area per year.

1. Write the equivalent logarithmic form for each of the models. There are directions for how to type math characters in the Resource Center that will show you show to enter logarithmic functions. What do the dependent and independent variables mean in this situation?

3. Describe the domain and range of each function and explain what the differences mean for the problem situation.

4. Compare the logarithmic bases of y₁ and y₂. What do these values tell you about their graphs?

5. Which two function graphs intersect? What is the point of intersection? Describe how the graphs are related before and after the point of intersection.

Solution

total cost = $11,000,000.

suppose number of users = x

therefore fee y = 11,000,000 / x

y = fee

b) domain is all values of x where function exists

therefore domain of this function is all values of x and x not equal to 0

interval notation ( -infinity , 0 ) U ( 0 , infinity )

range is all y values where function exists

range is all values of y except y = 0

interval notation ( -infinity , 0 ) U ( 0 , infinity )

c) domain is all x values and range is all y values

since in any rational function we cannot divide by 0 hence the 0 point is excluded in both domain and range

d) horizontal asymptote is y = 0

vertical asymtote x = 0

e) the meaning of asymptotes here is that number of users cannot be zero

because if number of users become zero the function will be undefined