Page 70 - Math SL HB Sem 1

Ft,]N(]'tIONS, EQUA'tIONS, INEQUAI,I'TIES

9- 'I'HE EXPONEN'I'lAL FTJNC'IION c'

'Ihe
=
,
exponential lunctions y er' *'here K is a nonzero constanl, are frequently used
as models ofexponential growth or decay.

For an example of exponential growth, interest compounded continuously uses the model
y p.e' where;
=
P is the initial investment
r is the interest rate as decimal
t is the time in years

f)efinitions

The function ,-roek' is a model lor 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 of the mineral
present at time t hours since the process started, is given by
M(t)= t4o12Y,t>o,k>O

where Mo is the original amount of mineral present. lt 128 kilograms of the mineral are reduced
to 32 kilograms in the first six hours ofthe process. Find:

a)
1. The value of k
2. The quantity of the mineral that remains after [ 0 hours of processing.

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

)- 1 ,