) If Daniella opens a mutual fund account with a deposit of $15,000 and it promises to pay an annual interest rate of r%, compounded on a monthly basis.
(i) Derive a function B, which shows the balance on Daniella′
s account the end of 6 years.
(ii) Make a comparison of the rates of change in B with resect to the interest rate when r is
8% , 10% and 12%.
(b) A virus is believed to be spreading through a sheep farm according to that equation
N = 450 (
1
1 + 249e
−0.1t ) where
N is the number of sheep infected and t is the number of days.
(i) How many sheep are infected at t = 0?
(ii) Using a spreadsheet calculate the number of sheep infected after 0, 10, 30 , 50, 70, 100 days)
(iii) Will all the sheep become infected eventually? Give reasons to support your answer.