Written Homework 1 1 1 1 3 1 6 Page 1 of 3 Math 140 PRINT YOUR NAME From the questions below please choose and solve 10 problems only The homework is worth 10 points Show all of your work and put a box around your nal answer Number each attempted question clearly Write legibly that is suitably large and suitably dark if the grader can t read your answer it s consider uncompleted Question 1 Let f x x2 For each of the following functions i state how the graph is related to the graph of f and ii use this information to draw the graph Question 3 Linear vs exponential data For each table of data examine the data and then take a guess as to whether the data would best be modeled by a linear or exponential function Once you make your choice see if you can write a function that models the data Question 2 Determine the domain of the function a g x f x 1 b h x f x 1 c l x f 5x d k x 5f x a g t t t2 9 b h x x x 1 x 3 x 4 2 Part A 0 x y 3 1 5 1 2 0 3 1 5 Part B Part C Part D x y x y x y 0 16 0 3 0 16 1 4 2 1 3 1 4 4 1 16 1 4 5 2 6 75 3 10 125 1 12 2 8 3 4 4 0 a two real roots b only one real root c no real roots that may be signi cant 2 a f x x2 1 Question 4 Roots of quadratic functions For which value s of b does the function f x x2 bx 1 have Question 5 Piecewise graphs Graph each of the given functions Be sure to clearly indicate possible points Math 140 Written Homework 1 1 1 1 3 1 6 Page 2 of 3 b g x 6 x 2 x 2 x2 x 2 x2 1 x 2 6 x 2 x 2 6 x 2 c h x d i x Question 6 Function composition Use the functions in Question 5 to answer the following a Find f g x and simplify your answer b Find g f x and simplify your answer Question 7 Let f t be the population in thousands of people of Math City as a function the time t in years In 2020 the population was 34000 and each year the where t 0 corresponds to the year 2020 population increases by 3000 people a Model the population by nding a formula for f t b Evaluate the expression f 6 and write a sentence explaining what this means c Solve the equation f t 64 and write a sentence explaining what this means Question 8 Let L f h be the amount of water in liters a species of tree needs per week when it is h meters tall A particular tree of this species in the PSU arboretum is hP meters tall and so it requires f hP liters of water per week and we de ne vP f hP a What is the practical meaning of the expression f hP 3 b What is the practical meaning of the statement f hP 1 vP 3 c What is the practical meaning of f hP 2 d What is the practical meaning of f hP 5 vP 2 Question 9 A spherical balloon with radius r inches has a volume V r 4 3 r3 a Find an expression for the amount of air required to in ate the balloon so that the radius increases b Find an expression for the amount of air required to double the radius of the balloon from a radius from r to r 3 of r to a radius of 2r c If the balloon starts with a volume of 36 cubic inches and the radius is increasing at 1 inch per minute then how long will it take for the balloon to in ate to a volume of 200 cubic inches Question 10 For each of the following scenarios determine what type of function linear or power ts the given description and nd a formula for y f x Assume for all the situations that y 1 when x 1 a Each time x increases by a factor of 2 y increases by a factor of 4 b Each time x increases by a factor of 2 y increases by a factor of 8 c Each time x increases by 1 y increases by 3 d Each time x increases by 1 y decreases by 3 e Each time x increases by a factor of 2 y decreases by a factor of 2 f Each time x increases by a factor of 2 y decreases by a factor of 4 Question 11 Let g t be the population in thousands of people of Calculus City as a function the time t in years where t 0 corresponds to the year 2020 In 2020 the population was 10000 and each year the population increases by 30 Math 140 Written Homework 1 1 1 1 3 1 6 Page 3 of 3 a Model the population by nding a formula for g t using the appropriate choice of a linear polynomial power trigonometric or exponential function or a piecewise combination thereof b Evaluate the expression g 6 and write a sentence explaining what this means c Solve the equation g t 16 9 and write a sentence explaining what this means Question 12 Let h t be the population in thousands of people of Algebra City as a function the time t in years where t 0 corresponds to the year 2020 In 2020 the population was 20000 Between 2020 and 2030 the population grows by 5000 people per year but then after 2030 the population declines by 8 per year a Model the population by nding a formula for h t using the appropriate choice of a linear polynomial power trigonometric or exponential function or a piecewise combination thereof b Evaluate the expression h 6 and write a sentence explaining what this means c Evaluate the expression h 12 and write a sentence explaining what this means Question 13 Population A is 20 thousand at t 1 where t is in years It grows by 15 per year a Find a formula for A t the population in thousands at time t b What is the doubling time The doubling time is the time it takes an exponentially growing function to double It s analogous to the half life of an exponentially decaying function Question 14 Answer the following parts a Write down a formula for the amount of money you would have in your account after t years if it started at 1000 and the account pays 2 5 annual interest compounded monthly b If you buy a car for 20 000 and it loses half its value every year when will the car be worth c A …