Exponential Functions

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Exponential Functions — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionDecayConcept Practice

4 marks~6 minCriterion A

A radioactive substance decays according to the model

y = 80(0.5)^{t/5}

, where

y

is the mass in grams and

t

is the time in years. The graph passes through the points

(0, 80)

(5, 40)

, and

(10, 20)

Deduce the half-life of the substance from the graph. [1]

Calculate the mass remaining after 15 years. [1]

A laboratory requires at least 15 g of the substance to conduct a valid experiment. Advise the laboratory whether the experiment can be conducted after 15 years, justifying your answer with reference to your calculated value. [2]

Solutions

2QuestionGraphing exponentialAssessment Practice

2 marks~3 minCriterion B

The graph shows two exponential functions: curve A,

y = 2^x

, and curve B,

y = \left(\dfrac{1}{2}\right)^x

.

Explain why the two curves are reflections of each other across the

y

-axis, using the relationship between the two functions. In your answer, state what this means for a general point

(a,\, b)

on curve A. [2]

Solutions

3QuestionBase interpretationAssessment Practice

4 marks~6 minCriterion C

Two bacteria strains are monitored in a laboratory. Strain A doubles every hour, modelled by

y = 2^x

, and Strain B triples every hour, modelled by

y = 3^x

, where

x

is time in hours.

Calculate the population of each strain at

x = 2

hours. [1]

Deduce the ratio of Strain B's population to Strain A's population at

x = 2

, and show how this ratio relates to the bases of the two functions. [2]

A lab protocol requires Strain B's population to be more than twice that of Strain A at all monitoring points. Justify whether this protocol should be considered reliable for all

x \geq 1

. [1]

Solutions

4QuestionDecayAssessment Practice

6 marks~9 minCriterion D

A patient receives a single 200 mg dose of a drug. The drug decays exponentially, with 88% remaining after each hour. The minimum effective concentration is 25 mg.

Construct an exponential decay model for the amount of drug

A(t)

remaining after

t

hours, in the form

A(t) = A_0\,e^{-kt}

, showing how you determine

k

. [2]

Deduce the hour at which the drug level first falls below 25 mg. [2]

Advise a clinician whether this model alone is sufficient to guide a repeat-dosing schedule, discussing at least two limitations and their implications for patient safety. [2]

Solutions

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