IB Maths AA SL 2.9 Exponential and Logarithmic Functions Questions

Practise IB Mathematics SL 2.9 by applying exponential and logarithmic functions methods to questions from the Question Bank.

Exam points

Analyse and graph exponential and logarithmic functions, including inverse relationships and asymptotes.
Solve exponential or logarithmic equations and interpret parameters using complete evidence.

[Maximum number: 6]

Let $f(x)=A \mathrm{e}^{k x}+3$ . Part of the graph of f is shown below.

Figure for Question IB Maths AA SL 2.9 Exponential and Logarithmic Functions Questions question 1 — IB Maths AA SL

The y-intercept is at (0,13).

(a)

Show that A=10.

[ 2 ]

substituting (0,13) into function
e.g. $13=A e^{0}+3$

13=A+3

(b)

Given that f(15)=3.49 (correct to 3 significant figures), find the value of k.

[ 3 ]

substituting into f(15)=3.49
e.g. $3.49=10 \mathrm{e}^{15 k}+3,0.049=\mathrm{e}^{15 k}$
evidence of solving equation
e.g. sketch, using ln
$k=-0.201\left(\right.$ accept $\left.\frac{\ln 0.049}{15}\right)$

(c)

Write down the equation of the horizontal asymptote of the graph f.

Let $g(x)=-x^{2}+12 x-24$ .

[ 1 ]

$\quad y=3$

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IB Maths AA SL 2.9 Exponential and Logarithmic Functions Questions question 1

Question (a)

Question (b)

Question (c)