Page 70 - Math SL HB Sem 1

I,-UNC'rrONS, ITQUATIONS, INEQTJAL[r'rES

'l
9. Hll IiXPONI,INTIAL F'llNC-'l'lON e'

The exponential lunctions y = eK' where K is a nonzero constant, are frequently used
,
as models ofexponential growth or decay.

For an example ol exponential growth, interest compounded continuously uses the model
y p.e" where;
=
P is the initial investment
r is thc interest rate as decimal
t is the time in years

Definitions

I-he fi-rnction y-yoc"' is a model for exponential growth if k>0 and a model for exponential decay
if k<0.
Example I
During the chemical processing of a particular type of mineral, the amount M kg ofthe mineral
present at time t hours since the process started, is given by
>
M(t) - Mo(2)k' ,/ 0,k > 0

where Mo is the original amount of mineral prcsent. lt 128 kilograms of the mineral are reduced

to 32 kilograms in the first six hours ofthe process. Find:

a)
1. The value oi,t
2. The quantity of the mineral that remains after I 0 hours of processing.

b) Sketch a graph of the amount of mineral present at time / hours after the process has started

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