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NY Regents Algebra II Exponential and Logarithmic Models — practice questions

Explore 5 free Exponential and Logarithmic Models questions in NY Regents Algebra II Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Exponential and Logarithmic Models questions and exercises with answers

Showing questions 1–5 of 5.

In an exponential model, what is the time taken for a quantity to double called?Read the answer and worked solution →In Newton's Law of Cooling, what does the constant Ts stand for?Read the answer and worked solution →In the logistic growth model, what does the constant c represent?Read the answer and worked solution →A sample holds 400 grams of carbon-14. About how much is left after 11,460 years?Read the answer and worked solution →Merge a culture through four hoursRead the answer and worked solution →

Worked practice questions

In an exponential model, what is the time taken for a quantity to double called?

  1. The doubling time
  2. The carrying capacity
  3. The cooling rate
  4. The order of magnitude
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Correct answer: A. The doubling time

1. Exponential growth multiplies a quantity by the same factor over equal time steps. 2. The length of time in which the quantity doubles is called the doubling time. 3. It is found by solving 2 times the starting amount equal to the starting amount times e to the power kt. _Source: OpenStax Precalculus (CC BY 4.0), section 4.7 Exponential and Logarithmic Models_

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In Newton's Law of Cooling, what does the constant Ts stand for?

  1. The starting object temperature
  2. The surrounding air temperature
  3. The continuous rate of cooling
  4. The temperature after one hour
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Correct answer: B. The surrounding air temperature

1. A cooling object levels off at the temperature of the air around it. 2. That levelling off is a horizontal asymptote in the model, and its height is Ts. 3. So Ts is the surrounding air temperature. 4. The starting difference between object and air is the constant A, not Ts. _Source: OpenStax Precalculus (CC BY 4.0), section 4.7 Exponential and Logarithmic Models_

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In the logistic growth model, what does the constant c represent?

  1. The starting population
  2. The rate of growth
  3. The carrying capacity
  4. The point of inflection
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Correct answer: C. The carrying capacity

1. Exponential growth never levels off, which is unrealistic over a long run. 2. The logistic model adds an upper bound that the outputs approach but never pass. 3. That upper bound is c, the carrying capacity. 4. The starting value is c divided by 1 plus a, so it is smaller than c. _Source: OpenStax Precalculus (CC BY 4.0), section 4.7 Exponential and Logarithmic Models_

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More Mathematics topics

Complex NumbersGraphs of Polynomial FunctionsPower and Polynomial FunctionsRational FunctionsZeros of Polynomial FunctionsProperties of LogarithmsQuadratic FunctionsDividing Polynomials