20. In "x" years from now, one investment plan will be generatingprofit at the rate of R₁ (x) = 50+ x² pesos per year, while a secondplan will be generating profit at the rate R₂ (x) = 200+ 5x pesos peryear. For how many years will the second plan be more profitable one?Compute also the net excess profit if the second plan would be usedinstead of the first.A. 15 yrs, P1687.50B. 12 yrs, P1450.25D. 10 yrs, P1360.25C. 14 yrs, P15640.25

Answered: 20. In "x" years from now, one…

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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If $11, 000 is invested at a rate of 3% per year compounded yearly, find value of the investment at each given time and round to the nearest cent. nt Use either )" or A A = P(1+ = Pe". n (a) after 10 months, A = $ Submit Answer Incorrect. Tries 6/99 Previous Tries (b) after 8 years, A = $ Submit Answer Incorrect. Tries 3/99 Previous Tries (c) after 76 years, A = $ ||
3. (W) On January 1, 2023, the market capitalization of Firm A was 5 billion dollars, and it increases by 20% every 5 years. On that same day, the capitalization of Firm B was 20 billion dollars, and it has a half life of 4 years. (a) Find a formula for A(t), the market capitalization (in billions of dollars) of Firm A, t years after January 1, 2023. (b) Find a formula for B(t), the market capitalization (in billions of dollars) of Firm B, t years after January 1, 2023. (c) When will the market capitalizations of the two firms be equal?
4. Two investments, A and B, produce a continuous income stream of 3%, compounded continuously. The rate of flow of income from investment A is f(t) = 2000e0.03t and the rate of flow of income from investment B is expected to be g(t) = 3000. (a) Find the total income produced by each of the two investments over the 5-year period. (b) Find the future value, the accumulated amount of money flow, of each of the two investments for 5 years. (c) Compute the interest earned by each investment over the 5-year period. (d) Find the present value of each of the two investments. (e) Interpret the answers determined in (a) to (d)
If $P is invested for n years at 12% compounded continuously, the future value that results after n years is given by the function S = Pe0.12n. (a) At what rate is the future value growing at any time (for any nonnegative n)? Your answer cannot be understood or graded. More Information = (u),s (b) At what rate is the future value growing after 1 year (n = 1)? S'(1) = %3D
4. A quantity of a radioactive element decays exponentially. On the 20th day of observation the amount of the radioactive element became twice smaller compare to the initial amount. On the 10th day of the observation the amount of the element was 50mg. Find: (i) the initial amount of the radioactive element; (ii) how many days is required in order initial one. have an amount that is ten times smaller than the
10. Isaac deposits $2,000 in a savings account with an annually compounded interest rate of 3%. The amount of money in the account in any year t after opening the account can be represented by the function f(t) = 2000(1.03)'. Isaac plans to take all of his savings out of the account in 3 6- years. How much money will he have in savings at that time? 4
The amount that should be set aside is $ (Round up to the nearest dollar.)
1. The purchasing power P (in dollars) of an annual amount of A dollars after t years of 5% inflation decays according to the following formula P=Ae^-0.05t A. How long will it be before a pension of $80,000 per year has a purchasing power of $20,000? (Round your answer to the nearest dollar). B. How much pension A would be needed so that the purchasing power P is $40,000 after 11 years? (Round to the nearest dollar). 2. Suppose the supply of x units of a certain product at price P dollars per unit is given by P= 17 + 5ln(2x+1) How many units of the product would be supplied when the price is $47 each (round your answer to the nearest whole number).
Please answer no. 4 only
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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