Question 5 In 1999, the population of Richmond-Petersburg, Virginia, metropolitan area, was 961,400 and wasincreasing at a at roughly 9200 people per year. The average annual income in the area was $30,593per capita, and this average was increasing at about $1400 per year. Use the product rule to estimatethe rate at which total personal income was rising in the area at this time. Explain the meaning ofeach term in the product rule.Question 6 Use Logarithmic differentiation to prove the product rule and the quotient rule. Hint: Let f(x) =A(x)B(x) and g(x) = C(x)/D(x) to start then take the natural log of both sides of each equation andthen take the derivative of both sides of the equation.Question 7 Use Logarithmic differentiation to find the derivative of a" for a positive constant a.

We need to estimate the rate at which total personal income was rising. NOTE -As per our…

Answered: Question 5 In 1999, the population of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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In a particular very small region, the consumer price index, C, depends on the current value of gross regional domestic expenditure E, number of people living in poverty P, and the average number of household members in a family F, by the following formula: e-EP C = 100 + F If it is known that the gross regional domestic expenditure is decreasing at a rate of PHP 50 per year, and the number of people living in poverty and the average number of household members in a family are increasing at 3 and 1 per year, resp., how fast does the consumer price index change per year at the moment when E = 1, 000, P = 200, and F = 5?
2015 2020 ITEM PRICE QUANTITY PRICE QUANTITY Cup of coffee 8.50 50 10.50 60 Toasted cheese sandwich 13.00 35 14.00 25 English muffin 9.00 120 9.50 138 The preliminary analysis of the data produced the following table: po qo p1 q1 poqo poq1 p1qo p1q1 8.50 50 10.50 60 425 510 525 630 13.00 35 14.00 25 455 325 490 350 9.00 120 9.50 138 1080 X 1140 1311 Σ W Y 2155 Using the table of analysis shown above, answer the following questions (use 2015 as the base year):
question 3
If the price of gold decreases at a monthly rate of 2.2%, by what percentage does it decrease in a year?
A certain city's power company charges their residents for electricity usage on a daily basis. There is a basic charge of 11.57 cents. For each day the first 10 kWh cost 4.81 cents per kWh and any additional kWhs are 9.69 per kWh. (A kWh, or kilowatt-hour, is a unit of energy.) (a) Complete the following table using the information provided above. kWhkWh 0 5 10 15 20 cost (dollars)cost (dollars) kWhkWh 25 30 35 40 cost (dollars)cost (dollars) (b) We can define a piecewise function f(x)f(x) where xx is the kWh used in a day and f(x)f(x) is the cost, in dollars. This function would have the form f(x)={g(x)h(x)ififx∈Ax∈Bf(x)={g(x)ifx∈Ah(x)ifx∈B What functions g(x)g(x) and h(x)h(x) make up the piecewise function f(x)f(x)? g(x)=g(x)= for A = h(x)=h(x)= for B = Hint: A and B are intervals. If an interval uses ±∞±∞ write inf or -inf . (c) Using the above function, what is the cost of 26 kWh? dollars. (d) For 3 dollars, what is the maximum kWh usage for one…
How’s this wrong? What’s the operating profit per meal?
In a given year, the U.S. federal income tax owed by a married couple filing jointly can be found from the following table. Married Filing Jointly Taxable Income $0-$18,550 T(x) = $18,551-$75,300 $75,301-$151,900 amount over $75,300 $413,351-$466,950 Tax Rate 10% $1,855 plus 15% of the amount over $18,550 $10,367.50 plus 25% of the $151,901-$231,450 amount over $151,900 $466,951 or more if $29,517.50 plus 28% of the $231,451-$413,350 amount over $231,450 $51,791.50 plus 33% of the $130,578.50 plus 39.6% of the amount over $466,950 (a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned. $111,818.50 plus 35% of the amount over $413,350 0 < x≤ 18,550 if 18,550 < x≤ 75,300 if 75,300 < x≤ 151,900 (b) Use the function to find T(40,000). $ (c) Find the tax due on a taxable inco of $90,000. $ (d) A friend tells Jack Waddell not to earn any money over $75,300 because it…
Above is a bar graph of (projected) total revenues in the global video streaming market from 2018 to 2026, in billions of U.S. dollars. What is the average annual growth rate from 2018 to 2026? Please convert your decimal to a percentage (i.e., 7.3 for 0.073) and then round to one decimal place. Incorrect answer:
Illustration 12.2. The sale of a commodity in tonnes varied from January 1961 to December 1961 in the following manner: 280 300 280 280 270 240 230 230 220 200 210 200 Fit a trend by the method of semi-average.
Give the growth factor that corresponds to 242% growth
The sales of a company rose to Rs. 120,000 in the month of January to Rs. 130,000 in the month of February while the seasonal indices for these two months were : 120 and 150 respectively. Was such an increment in sales satisfactory ? If not, what should have been the sale in the month of February to keep pace with the seasonal index.

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