functions 1. Sketch the graph of the following exponential functions. Determine the domain, range, and horizontal asymptote. a) v(x) = + 2 b) v(x) = 3(741) 2. From the dawn of humanity to 1830, world population grew to one billion people. In 100 more years (by 1930) it grew to two billion, and 3 billion more were added in only 60 years (by 1990). In 2013, the estimated world population was 7,1 billion with a relative growth rate of 1.1%. 0. a) Write an equation that models the world population growth, letting 2013 be year b) Based on the model, what is the expected world population (to the nearest hundred million) in 2025? In 2035? 3. BanxQuote operates a network of websites providing real-time market data from leading financial providers. The following rates for 12-month certificates of deposit were taken from the websites: a) Stonebridge Bank, 0.95% compounded monthly b) DeepGreen Bank, 0.80% compounded daily c) Provident Bank, 0.85% compounded quarterly Compute the value of $10,000 invested in each account at the end of 1 year. Logarithmic functions 4. Sketch the graph of the following logarithmic functions. Determine the domain, range, and horizontal asymptote. a) y(z) = 1 - In(z) b) y(z) = In(x + 1) 5. In its first 10 years the Gabelli Growth Fund produced an average annual return of 21.36%. Assume that money invested in this fund continues to earn 21.36% com- pounded annually. How long (to the nearest year) will it take money invested in this fund to double? SURVEY OF CALCULUS Prerequisite test Business problems 6. A shop wants to seel T-shirts. The owner recalls that there is a fixed cost and variable cost, although he does not remember the values. He does know that the T-shirt printing company charges $440 for 20 shirts and $1000 for 100 shirts. a) Find the equation C = f(r) that describes the total cost as a function of number of shirts. b) Determine how many shirts he must sell to break even if he sells the shirts for $10 each. 7. A baseball is hit straight up at 140 feet per second. The height of the ball when it was hit was 4 feet. The height of the ball above the ground as a function of time can be modeled by h(t) = -16t' + 140t + 4 a) When does the ball reach the maximum height? b) What is the maximum height of the ball? c) When does the ball hit the ground? 8. According to the World Bank, at the end of 2013 (t=0) the U.S. population was 316 million and was increasing according to the following model: P(t) = 3160-0074t where P is measured in millions of people and t is measured in years after 2013. a) Based on this model, what will be the population of the United States in 2020? b) Determine when the U.S. population will be twice what it is in 2013. 9. A human skeleton is found in an archeological dig. Carbon dating is implemented to determine how old the skeleton is by using the equation y = e", where y is the percentage of radiocarbon still present in the material, t is the number of years passed, and r = -0.000121 is the decay rate of radiocarbon. a) If the skeleton is expected to be 2000 years old, what percentage of radiocarbon should be present? b) For another skeleton there is 25% radiocarbon. How old is this new skeleton
