The function f(x) = 0.00056(3x + 2) + 1 models the Harrington PaperCompany's revenue, where x is the time measured in weeks and f(x) is therevenue measured in thousands of dollars. At what rate was the company'srevenue growing from week 50 to week 75?

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Answered: The function f(x) = 0.00056(3x + 2) + 1…

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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Suppose that a new employee starts working at $7.66 per hour, and receives a 5% raise each year. After time t, in years, his hourly wage is given by the function P(t) = 57.66(1.05)'. a) Find the amount of time after which he will be earning $10.00 per hour. b) Find the doubling time. After what amount of time will the employee be earning $10.00 per hour? |years (Round to the nearest tenth of a year.) What is the doubling time? years (Round to the nearest tenth of a year.)
The population of a town in Texas is modeled by the function f(x)=16,869(1.037)x. If the initial population (that is, the population when ( x=0) was measured January 1, 2014, what was the initial population?
3. Jeff Jefferson invested $2000 in an account that doubles in value every 5 years. The function that models the growth of his investment is f(x) = 2000-2*, where x is the number of doubling periods. If he leaves the money in the account, how much will he have after 20 years.
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Having completed your first few tasks, you move now to a portion of the lab where important bacteria are being grown. Based on the data collected, you have determined that the population of this bacteria in the range measured can be modeled as A (t) = 195(1.31)t, where t is given in days. To the nearest whole number, what will the bacteria population be after 5 days? The bacteria population will be Number
The projected number of people aged 65 and over in the U.S. population with Alzheimer’s disease (in millions) is given by the function: P(t) = -.0002083t3 + .0157t2 - .093t + 5.2 for (4 < t < 40) where t is measured in years, and t = 4 corresponds to 2014. What is the projected number of people aged 65 and over with Alzheimer’s disease in 2030? In 2050?
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A mobile phone company records their annual sales on 31 December every year. Paul thinks that the annual sales, S million, can be modelled by the equation S= ab', where a ar b are both positive constants and t is the number of years since 31st December 2015. Paul tests his theory by using the annual sales figures from 31t December 2015 to 31st Decemb 2019. He plots these results on a graph, with t on the horizontal axis and log,,S on the vertic axis. (a) Explain why, if Paul's model is correct, the results should lie on a straight line of best fit on h graph. The results lie on a straight line of best fit which has a gradient of 0.146 and an intercept on vertical axis of 0.583. (b) Use these values to obtain estimates for a and b, correct to 2 significant figures. (c) Use this model to predict the year in which, on the 31st December, the annual sales wvould fi be recorded as greater than 200 million. (d) Give a reason why this prediction may not be reliable.

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The function f(x) = 0.00056(3x + 2) + 1 models the Harrington Paper Company's revenue, where x is the time measured in weeks and f(x) is the revenue measured in thousands of dollars. At what rate was the company's revenue growing from week 50 to week 75?