Word Problems/Interest


QUESTION: Find the slope and vertical axis intercept of the linear functions, sketch the graph.
a. G(t) = 2(4 t)
b. 0.5q + 0.25

ANSWER: Note that linear functions are not quadratic.

g(t) = 2(4 - t) = -2t + 8
Slope = -2
vertical intercept = 8
f(q) = 0.5q + 0.25
slope = 0.5
vertical intercept = 0.25

---------- FOLLOW-UP ----------

QUESTION: Cities A and B presently have populations of 90,000 and 42,000 respectively. City A grows at the rate of 4% per year, and B grows at a rate of 12% per year. Determine the difference in the populations of the cities at the end of five years. How many years will it take City B to have the same population as City A?

Population of A after 5 years = 90,0001.04⁵ ≅ 109,499
Population of B after 5 years = 42,0001.12⁵ ≅ 74,018
Population of A after n years = 90,0001.04ⁿ
Population of B after n years = 42,0001.12ⁿ

B has the same population as A when 42,0001.12ⁿ = 90,0001.04ⁿ. Solve for n/
42,0001.12ⁿ = 90,0001.04ⁿ
1.12ⁿ/1.04ⁿ = 90,000/42,000
(1.12/1.04)ⁿ = 15/7
(14/13)ⁿ = 15/7

Take log base (14/13) of both sides of equation.
n = 10.2841844123 years

Population of A after 10.2841844123 years ≅ 134,715
Population of B after 10.2841844123 years ≅ 134,715

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Janet Yang


Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.


I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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