MATH 111 – FINAL EXAM Hints and Answers
Autumn 2007
1. (a) HINT: Draw the least steep diagonal line that intersects TC and compute its slope.
ANSWER: approximately $6.67 per Krumpette
(b) HINT: Draw a diagonal line with slope 11 and find the quantity at which it intersects
AC.
ANSWER: approximately 5.8 Krumpettes
(c) HINT: Draw the line tangent to TC (or V C) at q= 15 and compute its slope.
ANSWER: approximately 12 dollars or dollars per Krumpette
(d) HINT: Sketch the graph of TR , a diagonal line with slope 7.5, and find the quantities
at which the T R graph is above the T C graph.
ANSWER: from about 10.6 to about 16.3 hundred Krumpettes
(e) HINT: Slide your ruler to find the quantities at which the tangent line to T C is parallel
to T R.
ANSWER: approximately 3.7 and 13.7 hundred Krumpettes
(f) HINT: Find the largest vertical gap between T R and T C (when T R is above TC ).
ANSWER: approximately 12.5 hundred dollars (or 1250 dollars)
2. (a) TRANSLATION: The average trip speed of the red car at t= 14 seconds is 1.29 feet
per second.
(b) TRANSLATION: R(5) −R(1) > R(6) −R(2)
(c) ANSWERS: F; F; T
3. (a) T C(q) = cq +f,T R(q) = pq
(b) HINT: Set T R(q)−T C(q) = 100 and solve for q.
ANSWER: q=100 + f
p−cPies
(c) HINT: Use your answer to part (b).
ANSWER: q= 140 Pies
4. (a) HINT: Evaluate H(0).
ANSWER: 15 feet
(b) HINT: The height of the rock is a quadratic whose graph is a parabola that opens down.
The greatest height the rock reaches is the “y”-coordinate of the vertex.
ANSWER: 24.77 feet
(c) HINT: The rock hits sea level when H(t) = 0.
ANSWER: 2.03 seconds
(d) HINT: The height of the second rock at time tis H(t−10).
ANSWER: −16t2+ 345t−1835
5. (a) HINT: The balance changes from an OLD value, A(3) = P(1.02)3, to a NEW value,
A(3.2) = P(1.02)3.2. Use the formula for proportionate change and simplify.
ANSWER: 0.004
(b) HINT: You have two options. Either use the fact that A(5) = P(1.02)5= 2345 to
compute your principal now (P= 2123.94) and then use that value to compute A(5.5).
Or just compute what a principal of $2345 would become after 0.5 years: 2345(1.02)0.5.
ANSWER: $2368.33
