Let f(t) be the number of US billionaires in year t.(a) Express the following statements in terms of f.(i) In 2001 there were 272 US billionaires.(ii) In 2014 there were 525 US billionaires.(b) Find the average yearly increase in the number of US billionaires from 2001 to 2014.Express this using f.(i) Solution:(c) Assuming the yearly increase remains constant, find a formula predicting the number ofUS billionaires in year t.(i)Solution:

Given query is to find average rate of change and formula which gives the number of billionaire.

Answered: Let f(t) be the number of US…

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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A Math 110 student decides to make monthly payments of $1,000 into a retirement account paying 9% interest per year compounded continuously. If the student continues to make these payments for 50 years, compute each of the following values. Account balance after 50 years (exact value): Account balance after 50 years (rounded to the nearest cent) Total of all deposits (exact value) = Total of all interest payments (rounded to the nearest cent) dollars = = dollars dollars dollars
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…
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A client’s orders are growing consistently at x% per year. A) If three years from now orders are 50% higher than today, what is the annual growth rate (x)? B) Write an expression (in terms of x) for how many years it will take until orders are double what they are currently

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