_______________
Math 1030
Total 100 points
Savings plan formula:
Loan payment formula:
Name
Please show all your work.
A=PMTx n [
APR n
Px(
‘
APR
)
PMT
=
[1—( i+)’]
I
Compound interest: A
=
P (i ± ni
Continuous compounding: A =
Exponential growth:
Q
=
Tdouble
70
— P
Q =Q
Exponential decay:
Q
=
Q x
(l)t/Thalf
70
Thaif
Q =Q
(print)
Logistic growth: current/logistic growth rate = r x (i — population carrying capacity)

1. (15 pts) A community of rats will double every 20 months.
a) (10 pts) How long will it take population to triple in size?
TD 2o mh b) (5 pts) If the original population is 75, what is the population size 3 years later?
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)±1
31
Answer
7-)7
Answer
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
d
1+n
Answer
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%
Answer ‘
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)
J5UOOcO+25
Mi
[i 3i4DPO 525 fr1] i 003
2L2 ii o
I lo
, n
3i5 DOD
PHF
——
O20 —o.2q2
Total closing costs l2
Monthly payment
Interest
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
-O4i-
cc
CC
CC/I

6. (23 pts) A certain medication breaks down in the human body (decreases) at a rate of 6% per hour.
(Note: Please include the units in your answer.) a) (4 pts) Find the approximate half-life.
b) (7 pts) Find the exact half-life.
hr5
202 lirs
Answer
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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Answer Answer
19’11
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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 inby
Circle one: cEEntia) linear
Circle one: er year. -crJ9i
Circle one: growth decay