AM-1551

Exponential and logarithmic models

A Math · Secondary 4 · Hard · Exponential and logarithmic models

The population

P

of a bacteria culture after

t

hours is modelled by

P = A e^{0.4t} + B

, where

A

and

B

are constants. Initially, there are 300 bacteria, and after 2 hours there are 900 bacteria. Find the values of

A

and

B

.

$A = \dfrac{600}{e^{0.8}-1},\ B = 300 - \dfrac{600}{e^{0.8}-1}$
$A = \dfrac{300}{e^{0.8}-1},\ B = 600 - \dfrac{300}{e^{0.8}-1}$
$A = \dfrac{600}{e^{0.4}-1},\ B = 300 - \dfrac{600}{e^{0.4}-1}$
$A = \dfrac{900}{e^{0.8}-1},\ B = 300 - \dfrac{900}{e^{0.8}-1}$

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