# a level maths help

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#1
The population, P, of bacteria in an experiment can be modelled by the formula P = 100e0.4t,
where t is the time in hours after the experiment began.

How many whole hours after the experiment began does the population of bacteria first exceed 1 million, according to the model?
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1 year ago
#2
ok so you need to set up the equation. you know P = population and you want to know when the population > 1,000,000

therefore:

1,000,000 > 100e^0.4t

rearrange and take logs to find the value of t.
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#3
Do I need to know what e is?
0
1 year ago
#4
(Original post by hollyeb3)
Do I need to know what e is?
e is most likely Euler's number. It's on your calculator
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1 year ago
#5
(Original post by have)
e is most likely Euler's number. It's on your calculator
lool how jarring. OP u dont need to know e because it gets removed after u find ln (ln= loge)
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1 year ago
#6
(Original post by hollyeb3)
Do I need to know what e is?
the "ln" button is the button for logarithm with base e, e being Euler's number which is irrational and transcendental (just like pi), equal to approx 2.71828.

Here's what you should know about e for A-level: which means it will come up loads in questions relating to rate of change, because for , the rate of change is equal to the value.  and just for fun 0
1 year ago
#7
(Original post by hollyeb3)
The population, P, of bacteria in an experiment can be modelled by the formula P = 100e0.4t,
where t is the time in hours after the experiment began.

How many whole hours after the experiment began does the population of bacteria first exceed 1 million, according to the model?
100e^0.4t > 1000000
I divide both sides by 100;
e^0.4t = 10000
now solve ?
0
1 year ago
#8
ln10000=0.4t
0.4t=9.21...
t=23
but p>1000000
so t=24
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