Oil is leaking from an uncapped well and polluting a lake. Ten days after the leak is discovered, environmental engineers measure the amount of oil in the water to be 200 gallons with a current inflow rate of 30 gallons per day. The leak is slowing so that on the tenth day, the inflow rate is decreasing by 5 gallons/day each day. Suppose A(t) is the amount of oil (in gallons) tdays after the leak is discovered. (a) Find the quadratic approximation for A(t) centered at t= 10. (b) Use your answer in the previous part to estimate the amount of oil in the lake at t= 12.

Oil is leaking from an uncapped well and polluting a lake. Ten days after the leak is discovered, environmental engineers measure the amount of oil in the water to be 200 gallons with a current inflow rate of 30 gallons per day. The leak is slowing so that on the tenth day, the inflow rate is decreasing by 5 gallons/day each day. Suppose A(t) is the amount of oil (in gallons) tdays after the leak is discovered. (a) Find the quadratic approximation for A(t) centered at t= 10. (b) Use your answer in the previous part to estimate the amount of oil in the lake at t= 12.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

See similar textbooks

Similar questions

What is the y -intercept on the graph of the logistic model given in the previous exercise?
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?
Explain the difference between the average rate of change of y as x changes a to b, and the instantaneous rate of change of y at x=a
Researchers recorded that a certain bacteria population declined from 700,000 to 400,000 in 5 hours after the administration of medication. At this rate of decay, how many bacteria will there be 24 hours from the start of the experiment?
Researchers recorded that a certain bacteria population grew from 100 to 500 in 6 hours. At this rate of growth, how many bacteria will there be 24 hours from the start of the experiment?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.