4/20/22, 1:40 PMCA-4.6 Applications of Exponential Growth and Deca-Jackie Reames
Student: Jackie Reames
Date: 04/20/22
Instructor: Jessica Poole
Course: Math 1314-4W08
Assignment: CA-4.6 Applications of
Exponential Growth and Deca
1. A sample of 500 g of radioactivelead-210 decays topolonium-210 according to the function A(t) = 500 e − 0.032t , where t is
time in years. Find the amount of radioactive lead remaining after (a) 3 yr, (b) 6 yr, (c) 20 yr. (d) Find thehalf-life.
( a) The amount of radioactive lead remaining after 3 yr will be
(Round to the nearest integer asneeded.)
g.
( b) The amount of radioactive lead remaining after 6 yr will be
(Round to the nearest integer asneeded.)
g.
( c) The amount of radioactive lead remaining after 20 yr will be
(Round to the nearest integer asneeded.)
(d) Thehalf-life is about
g.
yr.
(Round to two decimal places asneeded.)
2. Find thehalf-life of a radioactiveelement, which decays
according to the function A(t) = A0 e
− 0.0132t
, where t is the
time in years.
Thehalf-life of the element is
years.
(Round to the nearesttenth.)
3. If 10 g of a radioactive substance are present initially and 2 yr later only 5 gremain, how much of the substance will be
present after 5 yr?
After 5 yr there will be
g of a radioactive substance.
(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as
needed.)
4. An employee wants to invest $60,000 in a pension plan. One investment offers 5% compounded quarterly. Another offers
4.25% compounded continuously.
( a) Which investment will earn more interest in 5 yr?
(b) How much more will the better planearn?
(a) After 5 years, (1)
will earn more interest.
(b) The better plan will earn $
(1)
more. (Round to the nearest cent asneeded.)
the 4.25% compounded continuously plan
the 5% compounded quarterly plan
5. How long will it take for an investment totriple, if interest is compounded continuously at 6%?
It will take
years before the investment triples.
(Round to the nearest tenth of ayear.)
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