Exponential Functions

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Exponential Functions — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionGrowthConcept Practice

2 marks~3 minCriterion C

A population of bacteria doubles every hour. A researcher models the population using

y = a \cdot b^x

, where

x

is time in hours. The population is 4 000 at

x = 1

and 8 000 at

x = 2

Deduce the value of

b

, the growth factor, showing your method. [1]

Interpret what the value of

b

means in the context of this bacterial population. [1]

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

3QuestionDecayConcept 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

4QuestionCompare growthAssessment Practice

2 marks~3 minCriterion D

A social media post goes viral. The number of shares is modelled by two competing predictions: a linear model

f(x) = 2x + 1

and an exponential model

g(x) = 2^x

, where

x

is the number of days after posting and the output is in thousands of shares.

A campaign is considered successful if it exceeds 10 thousand shares by day 5.

Calculate

f(5)

and

g(5)

. [1]

Both models predict a successful campaign. Justify which model a campaign manager should rely on for long-term planning, and defend your choice using the day-5 values and the growth behaviour of each model. [1]

Solutions

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