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,Â đ¶, of producing 𝑛 calculators? Linear Exponential Neither

(b) A colony of bacteria starts with 300 organisms and doubles every week. What would be the total population, 𝑃, of the bacteria colony after 𝑡 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,Â đ¶, of one year of college 𝑡 years after 1998? Linear Exponential Neither

(d) Assume the height, ℎ of a right triangle is equal to its base, 𝑏. What is the area of the triangle, 𝐮, in terms of its base 𝑏? (Area of a triangle =12 base ×height.) 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