An economist tracks the price of a certain item at the beginning of several years and compiles the following table.2014 2015273.47 281.672016290.122013YearPrice in dollars 265.50(a) Show that the price is growing as an exponential function. (Let P be the price in dollars and t the time in years since 2013.)Calculate the ratios of new price/old price. (Round your answers to two decimal places.)P₁.PoP2,P1P2Does the table show exponential data?YesNo(b) Find an exponential model for the data. (Round the values to two decimal places. Let t be the time in years since 2013.)CP= 304.21 x 0.83tP = 290.12 x 0.97tCP= 260.00 x 1.12tP = 93.12 x 1.35*P = 265.50 x 1.03t(c) At the beginning of some year, the price will surpass $344. Use the model found in part (b) to determine which year.

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Answered: An economist tracks the price of a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An economist tracks the price of a certain item at the beginning of several years and compiles the following table. Year 2013 2014 2015 2016 Price in dollars 265.50 273.47 281.67 290.12 (a) Show that the price is growing as an exponential function. (Let P be the price in dollars and t the time in years since 2013.) Calculate the ratios of new price/old price. (Round your answers to two decimal places.) P1 = P0 P2 = P1 P3 = P2 Does the table show exponential data? YesNo (b) Find an exponential model for the data. (Round the values to two decimal places. Let t be the time in years since 2013.) P = 290.12 × 0.97t P = 304.21 × 0.83t P = 265.50 × 1.03t P = 260.00 × 1.12t P = 93.12 × 1.35t (c) At the beginning of some year, the price will surpass $325. Use the model found in part (b) to determine which year.
2. For each of the following, X represents Rx R. Prove that each of the following distance function is a metric on X. Let x = (x₁, x₂), y = (91, 92) and z (21, 22) = (i).d(x, y) = √(x₁ - y₁)² + (x2 − y2)² (Hint: Use the Minkowski's Inequality: Σ(an + bn)² ≤ √Σan² + √b² where an, bn are real numbers. (ii). d(x, y) = (iii). d(x, y) = max {x1y₁, x2 - y2|}. - x₁y₁| + x2 - y₂| - 3. Extend each of the above three distance functions to define on XR and show that in each case the distance function is a metric.
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s IP☆回 Add-ons Help Last edit was seconds ago Background Layout - Theme Transition | 3 I 4 I 5 I 6 II 7 I 8 Name Date Basic Exponential Word Problems - Independent Practice The most recent flu virus is making people sick quickly. On the first day of the illness only 4 people at school had confirmed cases. Each day after, the amount of the flu cases quadruples. 1. Write a function that models the flu virus's growth over time. Use x for days and y for the amount of flu cases. Find the number of flu cases present by the 6th day. 2. A car cost $22,000 and will depreciate in value by 14% each year. Write a function that models the value of the car over time. Use x for years, and y for the value of the car, in dollars, Find the value of the car at the end of 5 years. Jim left an old hot tub full of water on his back porch during the summer. One night two mosquitos came to visit the hot tub. Each night after, there were three times as many 3. mArniiitersroond th hot tih otes
answer 9 and 10 using the information
Betty and Bob invest $2,000 in an account. a. After 8 years the account balance is $6,129.71. Find their per annum continuous rate of return. Your final answer should be correct to 2 places after the decimal point. ______________ b. If the trend continuous then find the account balance after 20 years. Your final answer should be correct to 2 places after the decimal point. _____________

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