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Temperature changes When an object is moved from one environment to another, its temperature T changes at a rate given by
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Mathematical Applications for the Management, Life, and Social Sciences
- Radioactive Decay The half-life of radium-226 is 1590 years. a If a sample has a mass of 150 mg, find a function that models the mass that remains after t years. b Find the mass that will remain after 1000 years. c After how many years will only 50 mg remain?arrow_forwardRadioactive Decay The half-life of radium-226 is 1590 years. (a)If a sample has a mass of 150 mg, find a function that models the mass that remains after tyears. (b)Find the mass that will remain after 1000 years. (c)After how many years will only 50 mg remain?arrow_forwardGrowth in Length of Haddock D.S. Raitt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula L=5342.820.82t a. Calculate L(4) and explain what it means. b. Compare the average yearly rate of growth in length from age 5 to age 10 years with the average yearly rate of growth from age 15 to age 20 years. Explain in practical terms what this tells you about the way haddock grow. c. What is the longest haddock you would expect to find anywhere?arrow_forward
- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forwardGrowth in Weight and Height Between the ages of 7 and 11 years, the weight w, in pounds, of a certain girl is given by the formula w=8t. Here t represents her age in years. a. Use a formula to express the age t of the girl as a function of her weight w. b. At what age does she attain a weight of 68 pounds? c. The height h, in inches, of this girl during the same period is given by the formula h=1.8t+40. i. Use you answer to part b to determine how tall she is when she weighs 68 pounds. ii. Use a formula to express the height h of the girl as a function of her weight w. iii. Answer the question in part i again, this time using your answer to part ii.arrow_forward
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