Exponential Functions
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Exponential Functions — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionBase interpretationConcept Practice
2 marks~3 minCriterion A
A population of bacteria in a laboratory experiment is modelled by y=a⋅bxy = a \cdot b^x, where yy is the number of bacteria (in thousands) and xx is the time in hours. The graph of this model passes through the points (0,3)(0, 3) and (1,6)(1, 6).
a
Deduce the value of aa. [1]
b
The laboratory considers the experiment viable only if the initial bacterial population exceeds 2500. Justify whether this condition is met. [1]
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2QuestionGraphing exponentialAssessment Practice
2 marks~3 minCriterion B
The graph shows two exponential functions: curve A, y=2xy = 2^x, and curve B, y=(12)xy = \left(\dfrac{1}{2}\right)^x.

Explain why the two curves are reflections of each other across the yy-axis, using the relationship between the two functions. In your answer, state what this means for a general point (a, b)(a,\, b) on curve A. [2]
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3QuestionBase interpretationAssessment Practice
4 marks~6 minCriterion C
Two bacteria strains are monitored in a laboratory. Strain A doubles every hour, modelled by y=2xy = 2^x, and Strain B triples every hour, modelled by y=3xy = 3^x, where xx is time in hours.
a
Calculate the population of each strain at x=2x = 2 hours. [1]
b
Deduce the ratio of Strain B's population to Strain A's population at x=2x = 2, and show how this ratio relates to the bases of the two functions. [2]
c
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≥1x \geq 1. [1]
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4QuestionGraphing exponentialAssessment Practice
8 marks~12 minCriterion D
A pharmaceutical company models the concentration of a drug in a patient's bloodstream as

C(t)=200⋅(0.85)tC(t) = 200 \cdot (0.85)^t

mg/L, where tt is the time in hours after injection. A nurse records the following measured concentrations:

Time (hours)1246
Measured concentration (mg/L)17014410475
a
Calculate the predicted concentration at each time point using the model. Present your results alongside the measured values. [2]
b
Calculate the percentage error at each time point using

% error=∣predicted−measured∣measured×100%\% \text{ error} = \frac{|\text{predicted} - \text{measured}|}{\text{measured}} \times 100\%

Round to one decimal place. [2]
c
Advise the nurse whether this model alone is sufficient for making clinical dosing decisions. In your response, discuss at least two limitations of the model and justify your advice by interpreting your percentage error results in a medical context. [4]
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