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Chapter 13 Solutions
Algebra and Trigonometry
- An arithmetic sequence has the first term a1=4 and common difference d=43 .What is the 6thterm?arrow_forwardPollution A chemical plant discharges 2400 tons of pollutants every year into an adjacent lake. Through natural runoff, 70% of the pollutants contained in lake at the beginning of the yare are expelled by the end of the year. (a) Explain why following sequence models the An. of the pollutant in the lake at the end of the nth year that the plant is operating. An=0.30An1+2400 (b) Find the first five terms of the sequence An. (c) Find a formula for An. (d) How much of the pollutant remains in the lake after 6 years? How much will remain after the plant has been operating a long time? (e) Verify to part (d) by graphing An with a graphing calculator for n=1ton=20.arrow_forwardA geometric sequence has the first term a1=3 and common ratio r=12 What is the 8thterm?arrow_forward
- Fitness Progam Sheila decides to embark on a swimming program as the best way to maintain cardiovascular health. She begins by swimming 5 min on the first day, then adds 112 min every day after that. Find a recursive formula for the number of minute Tn that she swims on the nth day of her program. Find the first 6 terms of the sequence Tn . Find a formula for Tn . What kind of sequence is this? On what day does Sheila attain her goal of swimming at least 65 min a day? What is the total amount of time she will have swum after 30 days?arrow_forwardPollution A chemical plant discharges 2400tons of pollutants every year into an adjacent lake. Through natural runoff, 70 of the pollutants contained in the lake at the beginning of the year are expelled by the end of the year. a Explain why the following sequence models the amount An of the pollutant in the lake at the end of the nthyear that the plant is operating. An=0.30an1+2400 b Find the first five terms of the sequence An. c Find a formula for An. d How much of the pollutant remains in the lake after 6years? How much will remain after the plant has been operating a long time? e Verify your answer to part d by graphing An with a graphing calculator for n=1 to n=20.arrow_forwardArithmetic Sequence? Find the first five terms of the sequence, and determine whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form an=a+(n1)d. 30. an=1+n2arrow_forward
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