math home work
FK1987
home_work_12.doc1. Solve the following equations:
(b)
5
53
x
-
=
(c)
log(9)2
x
-=
(d)
2
log(49)2log(23)
xx
-=+-
(e)
21
45
xx
+
=
2. Give a value for
7
log23
(i.e. something you could punch into a calculator and get the answer.)3. The half life of the polonium isotope
210
Po
is 140 days. If you start with 10 milligrams, how much will be left at the end of a year?4. How much money should be invested at 4.5% per year, compounded quarterly, in order to have $5000 in 6 years.
5. At what annual rate should you invest your money if you want it to triple in 20 years (assume continuous compounding) ?
6. An insect colony grows exponentially from 100 to 1500 in 2 months time. If this growth pattern continues, how long will it take the insect population to reach 100,000?
7. If
2
5
4
log16160
x
=
, then what is x? (Note, the exponent of the 16 is2
5
x
)8. If 0 < b < 1 draw a rough graph of
()1
x
gxb
=+
