Ex1b Please help with this also
Be sure to include units. All answers should be EXACT with all work shown. 1. A baseball hit by a batter at t = 0 has height given by H = -16t' + 64 + 4, where H is measured in feet and & is measured in seconds. (a) When is the baseball at its maximum height? (b) What is the baseball's maximum height? (c) Calculate the average vertical velocity of the baseball on the interval [0, 2]. 2. A cell phone data plan has a base charge of $40 per month. The plan includes 4 free gigabytes (GB) of data and charges $5 for each additional GB of usage. Let B = /(d) be the bill, in dollars, for using d gigabytes of data in a month. (a) Find a formula for f(d). (b) What does the expression f(5 + 2) represent? Circle one of the following. (i) the bill for using 5 + 2 gigabytes of data (ii) a dollars more than the bill for using 5 gigabytes of data (iii) the bill for using 5 gigabytes of data plus the bill for using a gigabytes of data (iv) 5 times the bill for using & gigabytes of data (c) What does the expression /(5) + 2 represent? Circle one of the following. (i) the bill for using 5 + 2 gigabytes of data (ii] a dollars more than the bill for using 5 gigabytes of data (iii) the bill for using 5 gigabytes of data plus the bill for using a gigabytes of data (iv) 5 times the bill for using r gigabytes of data (d) What does the expression f-(52) represent? Circle one of the following. (i) the approximate change in the bill between using 52 and 53 gigabytes of data (ii) the bill for using 52 gigabytes of data (iii) the gigabytes of data used for a bill of $52 (iv) the approximate change in data usage between a bill of $52 and $53 3. A particular person's height oscillates throughout the day with a period of 24 hours. Their average height is 155 em, and their maximum height is 157 cm. At 2AM, their hight is 155 em and increasing. (a) Find a possible formula for h(t), their height (in cm) & hours after midnight. (b) Find a time when their height equals 154.5 cm. 4. City A has a population of 3 million at t = 0, where t is measured in years, and doubles every 15 years. City B has a population of 10 million at f = 0 and is decreasing at a rate of 8% per year.(a) Find the formula for the population A(t) of City A (in millions of people) as a function of time t (in years). (b) Find the formula for the population B(t) of City B (in millions of people) as a function of time t (in years). (c) When are the populations of the two cities equal? 3 5. Let /(2) = /7 - 2(13-9) Find the domain of f, and express your answer in interval notation
