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Exponential and Logarithmic Functions · Paper 1 — Free Maths AI SL Practice Questions

1FoundationSAQ-SExponential functions and their graphs5 marksPaper 1~8 min

The graph of an exponential function

f(x) = a \times b^x

passes through the points

(0, 8)

and

(2, 32)

(a)

State the value of

a

. [1 mark]

(b)

Calculate the value of

b

. [2 marks]

(c)

Determine the value of

x

for which

f(x) = 8192

. [2 marks]

Solutions

2FoundationSAQ-SExponential functions and their graphs5 marksPaper 1~8 min

The graph of

f(x) = 3 \times 2^x

is shown for

-2 \leq x \leq 5

(a)

State the

y

-intercept of the graph. [1 mark]

(b)

Calculate the value of

f(2)

. [2 marks]

(c)

Find the value of

x

for which

f(x) = 96

. [2 marks]

Solutions

3MasterySAQ-SExponential functions and their graphs5 marksPaper 1~8 min

A colony of penguins on a remote island has a population modelled by

P(t) = 1200 \times (1.03)^t

where

P

is the population and

t

is the number of years after 1 January 2010.

(a)

State the population of the colony on 1 January 2010. [1 mark]

(b)

Calculate the population 1 January 2020, giving your answer to the nearest whole number. [2 marks]

(c)

Determine the year in which the population first exceeds

2000

. [2 marks]

Solutions

4ChallengeSAQ-LExponential functions and their graphs8 marksPaper 1~12 min

The graph of an exponential function

f(x) = a \times b^x + c

passes through the points

(0,\,7)

(2,\,15)

, and

(4,\,39)

(a)

Determine the values of

a

b

, and

c

. Give

b

correct to 3 significant figures. [4 marks]

(b)

Write down the equation of the horizontal asymptote of

f(x)

. [1 mark]

(c)

The parameter

c

is increased by 5 to give a new function

g(x) = a \times b^x + (c+5)

. Determine the coordinates of the

y

-intercept of

g(x)

. [1 mark]

(d)

A student claims that increasing

c

by 5 does not change the rate at which

f(x)

grows for large values of

x

. Justify whether this claim is correct. [2 marks]

Solutions

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