3.
A curve has equation: Y=1/[(x^2)+1]
The shaded region R is bounded by the curve, the coordinate axis and the line x=2.
a) Use the trapezium rule with 4 strips of equal width to estimate the area R.
[DONE this and got 1.10 to 3sfg]
The cross-section of a support for a bookshelf is modelled by R with 1 unit on each axis representing 8 cms. Given that the support is 2 cm thick,
b) Find an estimate for the volume of the support
4.
Amy plans to join a savings scheme in which she will pay in £500 at the start of each year.
One scheme that she is considering pays 6% interest on the amount in the account at the end of each year.
For this scheme,
a) find the amount of interest paid into the account at the end of the second year,
b) show that after interest is piad at the end of the 8th year, the amount in the account will be £5246 to the nearest pound.
Another scheme that she us considering pays 0.5% interest on the amount at the end of the each month.
c) find, to the nearest pound, how much more or less will be in the account at the end of the 8th year under this scheme.
Answers
a) £61.8
b) £5246
These are correct
for c) here is what I did
96 months in 8 years
Start Month 1 = 500
End month 1 = 500 * 1.005
Start month 2 = (500 * 1.005)+500
End month 2 = [(500*1.005)+500]*1.005
SO end month 2 = 500 * 1.005^2 + 500 * 1.005
= 500(1.005 + 1.005^2)
Therefore:
Sn = [a(r^n-1)] / (r-1)
Sn = 500* [1.005(1.005^96 - 1) / (1.005 - 1)
Sn = 61721.342
BUT
the answer is 5285.71
Therefore I cant calculate the difference
What they did
They said (1.005)^12 = 1.0617
and then said first term = 1.0617, n = 8, r = 1.0617
I don't understand their method.