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3.4 - 3.4 A chemical substance has a decay rate of 3.3 per...

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Unformatted text preview: 3.4 A chemical substance has a decay rate of 3.3% per day. The rate of change of an amount N the chemical is given by the equation dN dt = — 0.088 N where tis the number of days since decay began. Complete parts a} through c}. :1] Let NU represent the amount of the chemical substance at t= 0. Find the exponential function that models the situation. Na) 2 ND 9 — UDSSt II} Suppose that 600 g of the chemical substance is present at t= 0. How much will remain after 2 days? After 2 days, 503 g will remain. (Round to the nearest Whole number as needed.) c} After how many days ‘will half of the 600 g of the chemical substance remain? After 7.9 days, half of the chemical substance will remain. The decay rate, k, for a particular radioactive element is 2.1%, Where time is measured in years. Find the half-life of the element. The half-life is 33.0 years. How old is an ivory tusk that has lost 22% ofits carbon-14'? The ivory tusk is 2062 years old. Find the present value of $5000 payable at the end of2 years, if money may be invested at 3% with interest compounded continuously. The present value of $5000 is $4203.32 . (Round to the nearest cent as needed.) Hoyt:r much money must you invest now at 4.2% interest compounded continuously in order to have $10,000 at the end of a years? You must invest $ 2542.24 . The sales, S, of a product have declined in recent years. There were 204 million sold in 1984 and 1.5 million sold in 1994. Assume the sales are decreasing according to the exponential decay mode], SE12) = SE a ‘1“. a) Find the value 1-; and write an exponential function that describes the number sold after time, t, in years since 1984. b) Estimate the sales of the product in the year 2002. c) In What year {theoretically} will only 1 of the product be sold '? a) Rounded to six decimal places, k: 0.491265. b) To the nearest unit, the total is 29462 . c) Only one unit Will be sold in the year 2023. The power supply of a satellite is a radioisotope (radioactive substance). The power output P watts (W II, decreases at a rate proportional to the amount present; P is given by the equation F = 57.- é, — CIJZID42t where t is the time, in days. a} How much power will be available after 304 days? 15.9 W (Round to one decimal place as needed.) 11} “What is the half—life of the power supply? 165 days (Round to the nearest integer as needed.) 1‘} The satellite's equipment cannot operate on fewer than 14 watts of power. How long can the satellite stay in operation? 334 days (Round to the nearest integer as needed.) [1} How much power did the satellite have to begin with? 57" W (Round to the nearest integer as needed.) ...
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