What is the product or (m+3)(M-3)
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A=future amount
P=present amount
r=rate in decimal
n=number of times per year compounded
t=time in years
how many years to double
basically
A=2P at t=?
so we can simplify and ignore the pricipal given and do
r=7%=0.07
n=2 (semiannualy means 2 times per year)
t=t
take the ln of both sides
divide both sides by ln1.035
times 2 both sides
use calculator
40.2976=t
nearest tenth
40.3
about 40.3 years
We're told (and we can confirm) that , so
is a linear combination of the other two vectors.
This means <em>H</em> is sufficiently spanned by ; no need for the third vector.
But this also means we can write either as a linear combination of
, and
as a lin. com. of
. So any set of these three vectors taken two at a time will span the subspace <em>H</em>. Hence all of b, c, and d are acceptable.