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Type: Multiple-Choice
Category: Exponents
Level: Grade 11
Standards: HSF-IF.C.8, HSF-IF.C.8b
Author: nsharp1
Created: 5 years ago

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Exponents Question

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A cup of coffee that has just been poured has a temperature of 210 °F. The temperature of the room is 75 °F. After 4 minutes, the coffee's temperature is 175 °F. The function T(t)=Ta+(T0-Ta)e-kt, for t≥0, can model the coffee's temperature as it cools, where Ta is the ambient temperature, T0 is the initial temperature, and k is the constant of decay.

Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b

Why are the numbers for the percent rate of change calculated in the previous two questions not the same?
  1. Because the calculations didn't use exact numbers, and therefore there are rounding errors.
  2. Because the function has an added constant (it is not of the form abx).
  3. Because the percent rate of change calculated from the different form of the function, T(t)=a⋅bt+c, is a general rate of change, which is not the same as the specific rate of change from t=1 to t=2.
  4. Because an exponential function is not constant, therefore its percent rate of change shouldn't be constant.