Evaluate. (Round your answer to two decimal places.) 3.7+e6.98.4 Traffic engineers study how long the yeliow light for a traffic signal should be. for one intersection, the number of seconds n required for a n1+20v+v100 If the approach speed is 80 feet per second (about 55 miles per hour), how long should the yellow light be? (Round your answer to two decimal placesi) The population of the United States from 1790 to 1860 is given by the following formula, where t is years since 1790 and N is the population, in millions. N=3.931.03t (a) What was the population in 1790 ? milion (b) Express the population in 1805 using functional notation. The following is a partial table of values for f=f(x). (Round your answers to two decimal places.) (a) Estimate the value of f(1) by averaging. (b) Find the average rate of change for f between x=0 and x=2. (a) Explain in practical terms what N(1989) means. It represents the total number, in miliions, graduating from high school in the United States in 1989. It represents the total number graduating from high school in the United States in 1989. it represents the total number, in milions, graduating from high school in the United States, from 1989 through 1991. It represents the percentage of high school seniors graduating from high school in the United States in 1989. It represents the percentage of high school seniors graduating from high school in the United States, between 1989 and 1991. Find its value. million students (b) Use functional notation to express the number of graduates in 1986. M( Estimate its value. (Round your answer to two decimat places.) (c) Find the average rate per year during the period 1989 to 1991 . (Round your answer to two decimal places.) million students per year (d) Estimate the value of N(1996) : (Round your answer to two decimal places.) million students The graph in the figure shows a population N=N(d), where d is the date. (a) Is the function increasing, decreasing, or neither for d from 2006 to 2016 ? increasing decreasing neither (b) When is the function concave down? The function is concave down from 2006 to 2012 . The function is concave down from 2010 to 2014 . The function is concave down from 2012 to 2016. The function is never concave down. When is the function concave up? The function is concave up from 2006 to 2012 . The function is concave up from 2010 to 2014; The function is concave up from 2012 to 2016. The function is never concave up. (c) At what date is there an inflection point? (Round your answer to the nearest year.) d= (a) Explain in general terms how the population N changes with time. The population grows rapidly at first and then the growth slows. Eventually it levels off. The population growth is level at first and then the growth becomes very ropid. It maintains the rapid growth. The population does not change with time. The population grows slowly at first and then the growth becomes more rapid. It maintains the rapid growth. The population grows rapidly at first and then the growth is exponential. It maintains the exponential growth. (b) When does the population reach 350 ? if = (c) When is the population increasing most rapidly? d= (d) What is the name of the point of most rapid population increase? inflection point secant limiting value minimum maximum You currently have $720 in your bank account, which pays no interest. You withdraw $32 each week. Find a formula for the balance B, dollars, in the account after t weeks. = For each of the following functions C=C(t), find the value of C(0), reporting the answer rounded to two decimal places. Use your calculator where it is appropriate. (a) C=0.7+2.74e0.35t C(0)= (b) c=0.04+0.59t12.36 C(0)= (c) c=t+1t1 C(0)= (d) C=90.51/5730 c(0)= If you borrow P doliars at a monthly interest rate of r (as a decimal) and wish to pay off the loan in t months, then the monthly payment M = = M P,r1t) can be calculated, in dollars, using the following formula. M=(1+r)t1Pr(1+r)t (a) Caiculate M(5500,0.01,23). (Round your answer to the nearest cent.) Explain in practical terms what your answer means. This volue is your monthly payment if you borrow $5500 at a monthly rate of 1% for 23 monthe. this value is your monthly payment if you borrow $5500 at a monthly rate of 0.23% for 1 months. this value is your monthly payment if you borrow $5500 at a monthly rate of 0.01% for 23 months: this value is your monthly payment if you borrow $5500 at a monthly rate of 23% for 1 months. (b) Express the monthly payment for a loan of $6000 at a monthiy rate of 0.9% paid over 35 months in functionat notation, and then calculate its value. (Round your answer to the nearest cent.) MC. The following is a partial table of values for f=f(x). (Round your answers to two decimal places.) (a) Find the average rate of change for f between x=0 and x=2. (b) Find the average rate of change for f between x=2 and x=4. (c) Use your answer to part (b) to estimate the value of f(4). fou rent a wedding venue for a cost of $3400. The cost includes a catered lunch for 50 guests. For each additional guest, though, the catered lunch costs $32. (a) What is the cost of the venue and lunch if you invite 100 guests? 5 (b) Find a formula showing the cost of the venue and lunch as a function of n, the number of guests. Assume that n is at least 50 . C= (c) The amount you have budgeted for the venue and catered lunch is $5500. How many guests can you invite? guests Suppose the function below describes a physical situation that makes sense only for numbers between 3 and 8. f=x3227x2+54x+7 For what value of x does f reach a minimum? x= What is the minimum value? Solve the following for x. 11x=9+x Find the maximum and minimum values of x2+90/x on the horizontal span of 1 to 5 . Be sure to include endpoint maxima or minima. (Round your answers to two decimal places.) maximum value minimum value 2+660.96t=30 Suppose the function below describes a physical situation that makes sense only for whole numbers between 3 and 9 feet. f=12xx219 For what value of x does f reach a maximum? x= What is the maximum value? The length of North Sea sole, a species of fist, min be determined using the ven tertalaref model chen beiove t=14.810.1060.631t Here t is age, in yedrs; and t is terigth, in inches. (a) Make a grapb of ivenus t. Incude valies of t frem 1 to 10 veari. (b) Use funstional notation to express the length of a 3-year-old sole. 4(1) Calculate the value. (Round your answer to two decmal piaces.) in (c) At what age will a sole be 8 inches long? (Round yout answer to the nearest whole number) yr (d) What is the firniting length for a North Sea sole? (Round your answer to one decimai piace.) in he profit P, in millions of dollars, that a manufacturer makes is a function of the number N, in millions, of items produced in a year, and he formula is as follows. P=10NN26.24 A negative quantity for P represents a negative profit-that is, a loss-and the formula is valid up to a level of 10 million items produced. (a) Express using functional notation the profit at a production level of 5 million items per year. p( ) (b) What is the loss at a production level of N=0 million items? million doliars. (c) Determine the two break-even points for this manufacturer - that is, the two production levels at which the profit is zero. (Round your answers to two decimal places.) million items (smaller value) million items (larger value) (d) Determine the production level that gives maximum profit. (Round your answer to two decimal places.) milionitems Determine the amount of the maximum profit. (Round your answer to two decimal places.) million dollars The three principal measures of temperature are Fahrenheit F. Celsius C, and Kelvin K. These are related by the formulas below. F=1.8C+32K=C+273.15 (a) Solve eoch of the equations for C. with respect to F=C= with respect to KC= (b) Find a formula expressing F in terms of K. F= (c) Find the formula expressing K in terms of F. K=1 (d) Express the temperature 0 degrees Celsius in terms of degrees fohrenheit and in terms of kelvins (degrees on the Kelvin heale). (Aound your answers to two decimal places.) "F (e) Express the temperature 74 degrees fahrenheit in terms of degrees Celsius and in terms of kelvins. (Round your answers to two decimal places.) C min mis a penati? e 4at persont Yea I res min Use the single-graph method to solve the following. (Note: There are three solutions. Find all three. Round your answers to two decimal places.) 0.9x0.5x3=0x=(smallestvalue)x=(Iargestvalue) 6x2yx+y(x,y)=(=10=0 A stack contains 5540 worth of paper money consisting of twenty-doliar bills and fifty-dollar bills. There-are 15 bills altogether. How many twenty-doliar bills and how many fifty-dollar bils are in the stack? twenties bilis fiftes bils Noed Help? You're mixing blue paint with yellow paint to get a total of 14 gallons of the mixture. You want to use 3 times as much yellow paint as blue paint. How many galions of each should you use? (Round your answers to one decimal place.) yellaw paint 9al blue paint gal