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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 = 90,000×1.04⁵ ≅ 109,499

Population of B after 5 years = 42,000×1.12⁵ ≅ 74,018

:::::

Population of A after n years = 90,000×1.04ⁿ

Population of B after n years = 42,000×1.12ⁿ

B has the same population as A when 42,000×1.12ⁿ = 90,000×1.04ⁿ. Solve for n/

42,000×1.12ⁿ = 90,000×1.04ⁿ

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

Check:

Population of A after 10.2841844123 years ≅ 134,715

Population of B after 10.2841844123 years ≅ 134,715

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