Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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suppose the amount of people eating hotdogs in Europe is given by the function f(t) =
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- In a certain state, the sales tax T on the amount of taxable goods is 7% of the value of the goods purchased (x), where both T and x are measured in dollars. (a) Express T as a function of x.T(x) = (b) Find T(220) and T(5.90). (Round your answers to two decimal places.) T(220) = T(5.90) =arrow_forwardWhen purchased, the height of a Japanese maple sapling is 14 inches. The tree is expected to grow 2.5 inches each month. Which function models the relationship between the height of the tree f(m) and the number of m months of growth? A) f(m) = 2.5m B) f(m) = 2.5m + 14 %3D f(m) = 14m + 2.5 D) f(m) = 2.5m - 14. %3Darrow_forwardThe life expectancy E of a main-sequence star depends on its mass M. The relation is given by the formula below where M is solar masses and E is solar lifetimes. E = M2.5 The sun is thought to be at the middle of its life, with a total life expectancy of about 10 billion years. Thus, the value E= 1 corresponds to a life expectancy of 10 billion years. (a) Does a less massive star have a longer or a shorter life expectancy than a more massive star? O longer O shorter (b) Spica is a main-sequence star that is about 7.3 solar masses. What is the life expectancy of Spica? (Round your answer to three decimal places.) 0.068 billion yr (c) Express using functional notation the life expectancy of a main-sequence star with mass equal to 0.5 solar mass. (Round your answers to one decimal place.) E 5.7 Calculate that value. 57 billion yr (d) Vega is a main-sequence star that is expected to live about 6.36 billion years. What is the mass of Vega? (Round your answer to two decimal places.) 1.19…arrow_forward
- On the basis of data for the years 1912 through 1992, the expected life span of people in a country can be described by the function f(x) = 12.663 In x+17.681 years, where x is the number of years from 1900 to the person's birth year. What does this model estimate the life span to be for people born in 1937? This model estimates that the life span for people born in 1937 is (Round to the nearest year as needed.) years.arrow_forwardThe wind-chill index is modeled by the function W=13.12+0.6215T−11.37v0.16+0.3965Tv0.16, where T is the temperature in degrees Celsius and v is the wind speed (in km/h). When T=215 and v=30, by how much would you expect the wind-chill index to drop if the temperature decreases by 1 degree? What if the wind speed increases by 1 km/h?arrow_forwardThe country of Benin in West Africa has a population of 9.05 million people. The population is growing at a rate of 3.1% each year. Which of the following functions can be used to find the population 7 years from now? A f(t) = (9.05 x 106)(1 – .31)7 В f(t) = (9.05 × 106)(1 + 0.31)7 C f(t) = (9.05 x 106)(1 – 0.031)7 D f(t) = (9.05 x 106)(1+ 0.031)7arrow_forward
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- In this example we considered the function W = f(T, v), where W is the wind-chill index, T is the actual temperature, and v is the wind speed. A numerical representation is given in this table. (a) What is the value of f(-20, 40)? What is its meaning? f(-20, 40) = , which means that if the temperature is -20°C and the wind speed is 40 km/h, then the air would feel equivalent to approximately °C without wind. (b) Describe in words the meaning of the question "For what value of v is f(-10, v) = -15?" The question is asking: when the temperature is °C? Answer the question. V = km/h Answer the question. T = (c) Describe in words the meaning of the question "For what value of T is f(T, 10) = -39?" The question is asking: when the wind speed is °C? °C °C, what wind speed gives a wind-chill index of E km/h, what temperature gives a wind-chill index of d 9:16 PM 9/26/2022arrow_forward4) The number of snakes on Snake Island in Georgian Bay any year is dependent on two sources. Every year, through reproduction, the number of snakes on the island increase by 40 individuals. Snakes caught on other islands are also transplanted to Snake Island. The frequency of transplantation depends on the year and can be modelled by the function g(x)=10sin x+30, where g(x) represents the number of individuals transplanted in year x. Determine a function that will model the population of snakes on the island and takes into account both reproduction and transplantation. π 6arrow_forwardExtreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =arrow_forward
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