maths exponential functions
posted by Josh
I have a maths assignment and i need help with this question my teacher is overseas at the moment and it is due when he gets back
The Population P, of penguins in a certain region of Antarctica can be modeled by the relation P=Po (2) t/90, where t is time, measured in months and Po is the initial number of penguins.
a) if there are 800 penguins in the region today, how many will there be in 2 years?
b) what does the value of 90 represent in this formula?
c) How long will it take before there are 12 800 penguins?
this is only the first question on the sheet so i need the working out because then i will be able to do the rest myself
thank you if you can help

MathMate
Exponential functions are indicated on typographical material as a small number written on the top right of the base, like:
2^{t/90}.
While this is relatively difficult to do in a post, we usually represent the same expression using straight typing as:
2^(t/90)
Do not forget the parentheses, because exponentiation takes precedence over multiplication/division.
So please check that the given formula is:
P=Po (2)^(t/90)
a.
Po=population today, so Po=800.
t=number of months, so t=24 for two years.
There leaves only one unknown,
P=800*(2)^(24/90)=962.4, say 963
b. 90 represents a factor for the rate of exponential growth. The bigger the factor, the slower the population grows.
c. "How long" means we need to find "t".
So
12800=800*(2)^(t/90)
12800/800=(2)^(t/90)
16=2^(t/90)
take log to the base 2:
log_{2}16=(t/90)
4=t/90
so t=4*90=360 months = 20 years, assuming the population grows unchecked.
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