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AS Mathematics7356

7356

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3.7 F: Exponentials and logarithms

 
Content
F1

Know and use the function

ax
and its graph, where
a
is positive.

Know and use the function

ex
and its graph.

 
Content
F2

Know that the gradient of

ekx
is equal to
kekx
and hence understand why the exponential model is suitable in many applications.

 
Content
F3

Know and use the definition of

loga⁡x
as the inverse of
ax
, where
a
is positive and
x≥0

Know and use the function

ln⁡x
and its graph.

Know and use

ln⁡x
as the inverse function of
ex

 
Content
F4

Understand and use the laws of logarithms:

loga⁡x+loga⁡y≡loga⁡(xy)
;
loga⁡x-loga⁡y≡loga⁡xy
;
kloga⁡x≡loga⁡xk

(including, for example,

k=-1
and
k=-12
)

 
Content
F5

Solve equations of the form

ax=b

 
Content
F6

Use logarithmic graphs to estimate parameters in relationships of the form

y=axn
and
y=kbx
, given data for
x
and
y
.

 
Content
F7

Understand and use exponential growth and decay; use in modelling (examples may include the use of

e
in continuous compound interest, radioactive decay, drug concentration decay, exponential growth as a model for population growth); consideration of limitations and refinements of exponential models.