Exponential and logarithmic modelling question thread(help)

[tolga]

Q)The intensity of light d metres below the surface of the sea can be modelled by the equation I=Ioe^-kd, Divers in the sea of Loga have found that the intensity of light is halved when a diver is 5 metres below the surface of the water:
a)Find the value of K correct to 4 decimal places.
b)Find the percentage of light available at a depth of 10 metres.
c)If artificial light is necessary when the intensity is less than 0.1 of the intensity of the surface(1<0.1Io), find how deep a diver can go before artificial light is necessary.

Q)The number of bacteria present in a culture at any time,t , hours, can be modelled by the equation N=Noe^kt.
a)If the original number is doubled in 3hours, find k correct to two decimal places.

Q)The decay of a radioactive substance can be modelled by the equation M=Moe^-kt, where M grams is the mass of the substance after t years. After 10 years the mass of the substance is 98 grams and after 20 years the mass is 96 grams.
a)What ws the mass of the substance initially?Give your answer to the nearest gram.


NOTE:e is euler's number and Mo and No  and Io is a term on its own meaning original amount.

[the.watchman]

QUESTION 1

a) Assuming that ,

, (4dp)

b)

c) ,

QUESTION 2

a) ,

QUESTION 3

a) For (10,98),

For (20,96),

Solving these simultaneously gives:

[tolga]

shouldn't it be I/2=e^-5k and why would you assume Io=1

[the.watchman]

shouldn't it be I/2=e^-5k and why would you assume Io=1

Just for proportions

[tolga]

for 1a why is it 1/2 instead of I/2 amd question 2 is 0.23

[the.watchman]

for 1a why is it 1/2 instead of I/2 amd question 2 is 0.23

Think of it more as skipping a step, becomes

Oops ... I subbed in 3 instead of 2 in question 2 ...

I just had dinner, so I'll finish it off now