6. g(a) = a² + 8a – 7 7. f(b) = (b + 6)(b – 2) %3D %3D 8. h(x) 2x+17 %3D 3x+1
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- If xis large, which function grows faster, f(x)=2x or g(x)=x2?Reduce the given equation into the form of a homogenous function then transform into a variable separable to obtain the required general or particular solutionAn article† in The New York Times states, "The number of gas stations [in a city] grows only in proportion to the 0.77 power of population." This means that the approximate number G of gas stations in a city is a power function of the population N, and the power is k = 0.77. That is, G = cN0.77, where c is some (as yet) unknown constant. We measure N in millions. (a) If one city is twice as large as another, how do the numbers of gas stations compare? (Round your answer to two decimal places) If one city is twice as large as another, it has about times as many gas stations. (b) The population of City A, is 2.5 million and there are 1235 gas stations in City A. Use this information to find the value of c. (Round your answer to two decimal places.) c = (c) City B has a population of about 3.8 million. Using the value of c that you found in part (b), estimate the number of gas stations in City B. Round your answer to the nearest whole number. gas stations
- Suppose the percent of males who enrolled in college within 12 months of high school graduation is given by y= -0.126x + 55.72 and the percent of females who enrolled in college within 12 months of high school graduation is given by y= 0.73x + 39.7, where x is the number of years after 1960. Use graphical methods to find the years after these models indicate that the percent of females equaled the percent of males.Find the second derivative of the function. h(x) = 6x−2 + 7x2This week a factory is producing 50 units of a particular commodity, and the amount being produced is increasing at the rate of 2 units per week. If C(x) dollars is the total cost of producing x units and C(x) = 0.08x3 − x2 + 10x + 4 , find the current rate at which the production cost is increasing.
- Eliminate the arbitrary constants on the given equationFind the 1st and 2nd derivative of : c1e^2x + c2xe^2xSuppose the percent of males who enrolled in college within 12 months of high school graduation is given by y =-0.126x+55.72 and the percent of females who enrolled in college within 12 months of high school graduation is given by y=0.73x+39.7, where x is the number of years after 1960. Use graphical methods to find the year these models indicate that the percent of females equaled the percent of males.
- A group of survivors on a supply run has returned to their base camp with a population of 2000. Two of them were bitten by zombies but didn’t tell anyone. If it is assumed that the rate at which the virus spreads is proportional not only to the number x of infected people but also to the number of people not infected, determine the number of infected residents after 14 days if it is further observed that after 6 days, 50 residents got infected. What is the time at which half of the population will become infected if nothing is done? How many people will be NOT be infected after 2 weeks if nothing is done? A rescue helicopter saved 40 survivors. How long did they have to survive?Find the 2nd derivative with complete solution y = 3x + 5 / x^2 + 4Solve the first and second derivative and eliminate the arbitrary constant. 1. y = C1x + C2e-x + x2
