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Study SL 2.9—Exponential and logarithmic functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 6]

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

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 Topic Practice

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Question 1

Question (a)

Question (b)

Question (c)