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General Information

Related Standards: MAFS.912.F-LE.1.1
Reporting Category: Functions: Linear, Quadratic, & Exponential Models
Type: : Multiple Types
Difficulty: N/A
Question:

The graph of function f models the specific humidity in the atmosphere, in grams of water vapor per kilogram of atmospheric gas begin mathsize 12px style left parenthesis fraction numerator g over denominator k g end fraction right parenthesis end style, versus temperature, in degrees Celsius (ºC), as shown. Four of its points are labeled.

This question has two parts.

Part A.

Felicia wants to model the raltionship between temperature, in ºC, and specific humidity, in begin mathsize 12px style fraction numerator g over denominator k g end fraction end style. Select words to complete the statement about the type of model Felicia should use.

The relationship is _____________ because the specific humidity increases by equal ______ over equal intervals of temperature.

Part B.

Which relationship must be true to justify the function type that models the relationship?

Answer Options:

Part B.

A. begin mathsize 12px style fraction numerator f left parenthesis 20 right parenthesis minus f left parenthesis 35 right parenthesis over denominator 20 minus 35 end fraction equals fraction numerator f left parenthesis 25 right parenthesis minus f left parenthesis 40 right parenthesis over denominator 25 minus 40 end fraction end style

B. begin mathsize 12px style fraction numerator f left parenthesis 25 right parenthesis over denominator 20 end fraction equals fraction numerator f left parenthesis 40 right parenthesis over denominator 35 end fraction end style

C.begin mathsize 12px style fraction numerator f left parenthesis 40 right parenthesis minus f left parenthesis 35 right parenthesis over denominator 40 minus 35 end fraction equals fraction numerator f left parenthesis 25 right parenthesis minus f left parenthesis 20 right parenthesis over denominator 25 minus 20 end fraction end style

D. begin mathsize 12px style fraction numerator f left parenthesis 40 right parenthesis over denominator 20 end fraction equals fraction numerator f left parenthesis 35 right parenthesis over denominator 20 end fraction end style

Possible Answer:

Part A. 

The relationship is exponential because the specific humidity increases by equal factors over equal intervals of temperature.

Part B.

B.


Aligned Standards

Code Description
MAFS.912.F-LE.1.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. ★
  1. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
  2. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
  3. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.


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