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Question 1 0 ( a ) The concentration of caffeine in the blood plasma of an adult t hours after they have consumed a 1

Question 10
(a) The concentration of caffeine in the blood plasma of an adult t hours
after they have consumed a 150 milligram dose of caffeine can be
modelled by the function: c(t)=15e-0.3t-15e-0.6t, for t0, where
the concentration, c(t), is measured in milligrams per litre (mgl).
Show that the concentration of caffiene in an adult's blood
plasma reaches its maximum at t=10ln23 hours.
(b) On the day Paul's grandson Ollie was born,Paul deposited 5000
into an account earning 3% per annum compounded annually. On each
birthday after this he deposited 1000 into the same account, making
his final deposit on Ollie's 17 th birthday. That is, a total of 18 deposits
were made. Let An be the amount in the account on Ollie's nth birthday
after the deposit n is made. Show that A3=8554.54
(c) Find the value of Ollie's account on his 17 th birthday, just after
the final deposit is made.
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