Math Problem Statement
Determine if the following scenarios could be modeled by a linear function, exponential function, or neither.
(a) Last year, Pinwheel Industries introduced a new model calculator. It cost $ 2000 to develop the calculator and $ 20 to manufacture each one. What would be the total cost, đ¶, of producing đ calculators? Linear Exponential Neither
(b) A colony of bacteria starts with 300 organisms and doubles every week. What would be the total population, đ, of the bacteria colony after đĄÂ weeks? Linear Exponential Neither
(c) In 1998, the average annual cost of attending a public college was $ 10,069, and costs were climbing by 6% per year. What would be the cost, đ¶, of one year of college đĄÂ years after 1998? Linear Exponential Neither
(d) Assume the height, â of a right triangle is equal to its base, đ. What is the area of the triangle, đŽ, in terms of its base đ? (Area of a triangle =12 base Ăheight.) Linear Exponential Neither
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Exponential Growth
Algebra
Geometry
Formulas
Linear Function: C(n) = 2000 + 20n
Exponential Function: P(t) = 300 * 2^t
Exponential Function: C(t) = 10,069 * (1.06)^t
Area of Triangle: A = (1/2) * b^2
Theorems
Linear Growth Model
Exponential Growth Model
Area of Triangle Formula
Suitable Grade Level
Grades 9-12
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