MATH 121 001 Calculus I for Natural Science, Social Science, and Business
Test 1
Dr. H. Edward Donley
September 18, 2015
Name
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + 𝑛)
1. (9 points) The mean global temperature in July 1910 was 15.4 oC. It has grown
approximately linearly and in July 2015 the mean was 16.6 oC. Find an equation for
the mean global temperature as a function of t, where t = 0 represents July 1900.
2. (9 points) The median age of the U.S. population is approximated with the linear least
squares line, y = 0.243x + 27.82, where x is years since 1970.
a) What are the units for the slope and what does it represent?
b) For this least squares line, R2 = 0.995. What does this mean?
c) Use this line to predict the median age of the U.S. population in the year 2020.
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3. (7 points) Suppose that a surveyor's marginal costs are $90 per job, and her total cost
for 12 jobs is $2000. Write an equation for the total cost of surveying x jobs. What is
the value of the fixed cost?
4. (8 points) How much money must be invested at 3% annual interest, compounded
quarterly, to have $10,000 in 12 years?
5. (9 points) The population of Canada is 35 million and it increases each year by 1.2%.
Write down an equation for the population t years from now and use logarithms to
determine when the population will reach 50 million.
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x  4x  3
x2  1
2
6. (11 points) Analytically find
lim
x  1
lim
7. (10 points) Find
x
7 x 3  200 x
8 x 3  3x  1
8. (10 points) Given the graph at the right, what is the value of:
y
a)
8
f(1)
6
lim
f ( x)

x 1
lim
f ( x)
c)

x 1
lim
f ( x)
d)
x 1
b)
4
2
2
1
0
1
x
2
e) Is f continuous at x = 1? If not, list which of the three requirements for continuity
are not met.
9. (7 points) Given the graph of f at the right, at what values of x
is f not differentiable? For each value of x, explain why f is not
differentiable.
y
1.0
0.5
1
1
0.5
1.0
2
3
x
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10. (7 points) The mass in grams of the human brain during the last trimester and the first
1500
two years after birth can be approximated by 𝑚(𝑐) = 0.01𝑐 3 − 𝑐 , where c is the
head's circumference in centimeters. Find the average rate of change of m with
respect to c from c = 30 cm to c = 50 cm. Include the units in your answer.
11. (12 points) Use the limit definition of the derivative to find the derivative of
f(x) = x2 – 3x – 9.