function by the 1) A radioactive substance decays in such a way that the amount
ID: 3137612 • Letter: F
Question
function by the 1) A radioactive substance decays in such a way that the amount of mass remaining after t days is given m()-13e 001s where mt) is measured in kilograms. (6 points) aj find the mass at time t hundredths) b) How much of the mass is left after 45 days. (Round to b) $where t years. Find the diameter cf 5.4 2) The diameter D in feet of a tree is given by the equation D)- where t - years. Find the diameter of a 20 year old tree. Show the set up, then use your cakculator. Round to 3 decimal places. (4 points) 3] if SA,000 is invested at a rate of 6.8% gewinthe setup, find the amount in the account after-(6 points) aj one year simple interest b)5 years, compounded quarterly c)5 years compounded continuously rite your 4) Express each in exponential form. (4 points) a) log, 4- b) In (x-1)-6 b)
Explanation / Answer
The image is very faint. Hence the answers are on a best effort basis.
a. The mass of a radioactive substance ( which decays), left after t days is given by m(t) = 13 e-0.015t. When t = 0, we have m(0) = 13 kg. ( as e0 = 1)
b. When t = 45, we have m(45) = 13e-0.015*45 = 13 e-0.675 = 13*0.50915642 = 6.619 kg ( on rounding off to the nearest gram) or, 6.62kg (on rounding off to the nearest hundredth).
2. The diameter of a t year old tree is given by D(t) = 5.4/[1+2.9e-0.6t]. When t = 20, we have D(20) = 5.4/[1+2.9e-0.6*20] = 5.4/[1=2.9e-12] = 5.4/(1+2.9* 0.00000614421] = 5.4/(1.000017818)= 5.3999 meters or, 5.400 meters( on rounding off to 3 decimal places).
3.a) The simple interest on $ 54000 @6.8 % for 1 year is $ 54000*6.8/100 = $ 3672. Hence, the required balance in the account is $ 54000 +$3672 = $ 57672.
b).The balance in the account, including interest for 5 years, compounded quarterly is 54000(1+6.8/400)5*4 = 54000(406.8/400)20 = 54000*1.400938461 = $ 75650.68 (on rounding off to the nearest cent).
c).The balance in the account, including interest for 5 years, compounded continuously, is 54000e(6.8/100)*5 = 54000e0.34 = 54000*1.404947591 = $ 75867.17(on rounding off to the nearest cent).
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