# Math 1030 Exam 2 Practice

```EXAM #2
Math 1030
Name
(print)
Total
100 points
Savings plan formula:
A=PMTx
[
Px(
PMT =
Loan payment formula:
‘
[1—(
Compound interest: A
=
P (i ±
I
n
APR
n
APR
)
i+)’]
ni
’
1
Continuous compounding: A = Pe’
Exponential decay:
Exponential growth:
Q=Q
0
t/Tdouble
2
70
Tdouble
—
P
(1+r)
0
=Q
Qt
Logistic growth:
Q=Q x
Thaif
(l)t/Thalf
70
(1—r)
0
=Q
Qt
current/logistic growth rate = r x (i
—
population
carrying capacity)
1. (15 pts) A community of rats will double every 20 months.
TD 2o mh
b) (5 pts) If the original population is 75,
what is the population size 3 years later?
a) (10 pts) How long will it take
population to triple in size?
-5322 21/5
2
31
• I599
7-)7
)±1
-í
2. (10 pts) One lucky day you meet a leprechaun who promises that he will give you 16 “magic pennies”.
Each of those pennies will double each day. So, on day 1 you will get 16 pennies from the leprechaun, on
day 2 you will have 32 pennies, on day 3 you will have 64 pennies, etc.
On what day will you have 229 = 536,870,9l2pennies?
2.
32
3 mft 1+n
-I-bc d
1
3. (12 pts) The diameter of a tree increases by 0.8 inch every 5 years. When you started observing the tree,
its diameter was 7 inches.
a) (6 pts) Write a linear equation that describes this situation.
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b) (6 pts) How long will it take for the diameter to be 13 inches?
13)nt
1
DJ%
4. (20 pts) You need a mortgage loan of \$315,000. You can get a 20 year fixed-rate at an APR of 3h5%,
with closing costs of \$600 and 1 .5 points. Determine your total closing costs, monthly payments over the
term of the loan (excluding the closing costs), and the amount of interest paid over the loan term (in \$ and
% terms).
P @E)
Mi
[i
Xj
-(
±
1
fr1]
i
003
——
PHF
J5UOOcO+25
O20
2L2
D
/
,
1
3i4DPO
ii
o
525
I lo ,
n
3i5 DOD
—o.2q2
Total closing costs l2
Interest
Monthly payment
Interest
(%)
I
27
5. (12 pts) Suppose that a country’s population is 35 million and its population current growth rate is
1.8% per year. If the population growth follows a logistic growth model with the base growth rate, r =
2.3%, what is the country’s carrying capacit ?
Oi x()23
O1r’.(o)= j
—I
CC
—I
-O4i-
-
CC
cc
CC/I mjl/iofl
/
6. (23 pts) A certain medication breaks down in the human body (decreases) at a rate of 6% per hour.
a) (4 pts) Find the approximate half-life.
b) (7 pts) Find the exact half-life.
hr5
202 lirs
T7.Jrc
c) (7 pts) How long does it take for the medica
tion to reduce to 16% of the original amount?
6-oo
d) (5 pts) If you took 75 mg of the medication at 8 am,
How much is left in your bloodstream at 5 pm
(the same day)?
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-i-
•- o)9
z5üs 525)
qt25
19’11
C,
7. (8 pts) Identify if each of the following models is exponential or linear, and if it represents growth or
decay.
a) Minimum wage in a small town has been increasing by \$O’ryear.
Circle one:
exponential
ar
b) The price of computers has beenf
linear
Circle one:
cEEntia)
inby
Circle one:
decay
er year. -crJ9i
Circle one:
growth
—79 r5
```
Pastoralists

20 Cards