6. Ten-year-old Kayla's lemonade stand has experienced rises and falls in sales caused by temperature changes over the last few summers. Her sales over the first two weeks of summer were tracked according to the model S(x) = x³ − 12x² + 36x, where x is the number of days and S(x) is the number of sales. a) Kayla makes a profit if she sells at least 10 glasses of lemonade. Use the model to determine the number of days that she made a profit. b) What are the domain and range? (2.6 11)

In 2017 the price of a particular earlier model car was about $15,905 with a depreciation of about $1,231 per year. A student had $500 in 2017 and saves $1,700 each year. a) Let H(t) be the value, in dollars, of the desired car t in years since 2017. Let S(t) be the student's total savings, in dollars, t years since 2017. Find equations of H and S.  b) Set up an equation to predict  when the student will be able to buy the car using cash from his savings. State the answer in terms of the year he can buy the car.  c) Now assume that the student earns intrest on his savings. Is your answer from part (b) an underestimate or overestimate? Explain.

graph the linear equation    f(x)=4x

Suppose a rumor is spreading that the government plans to give each college student $1000. Asssume that 20 people have heard the rumor as of today and that each day the number of people (past and present) who have heard it triples. Let f(t) be the number of people (past and present) who have heard the rumor at t days since today. a. Find an equation of f. b. How many people (past and present) will have heard the rumor 10 days from now? c. How many people (past and present) will have heard the rumor 15 days from now? Has model breakdown occurred? [Hint: Assume that the population is 112 million.] a. Find an equation of f. f(t) = ¹ b. How many people (past and present) will have heard the rumor 10 days from now? people c. How many people (past and present) will have heard the rumor 15 days from now? people Has model breakdown occurred? A. Model breakdown has occurred because the value for f(15) is greater than the population. B. Model breakdown has not occurred because the value for…