A radioactive substance decays in such a way that the amount

A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 13e^-0.015t where m(t) is measured in kilograms. a) find the mass at time t = 0 b) How much of the mass is left after 45 days. The diameter D in feet of a tree is given by the equation D(t) = 5.4/1 + 2.9e^-0.01 t where t = years. Find the diameter of a 20 year old tree. Show the set up, then use your calculator. If $4,000 is invested at a rate of 6.8% showing the setup, find the amount in the account after... a) one year simple interest b) 5 years, compounded quarterly c) 5 years compounded continuously Express each in exponential form. a) log_8 4 = 2/3 b) In (x - 1) = 6

Solution

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Given
m(t) = 13 e^ (-0.015t)
a) Mass at time t = 0 can be computed by substituting t=0 in the given equation
m(0) = 13 e^0
m(0) = 13 Kg
b) Mass left after 45 days
=> t = 45
m(45) =	13 e^ (-0.015*45)
m(45) =	6.619033	kg
	Solution