SOLUTION: A certian population obeys the latural law of decay. at a certian time,the population is 40,000. three years later the population is 38000. approximately how long does it take the
Algebra.Com
Question 327293: A certian population obeys the latural law of decay. at a certian time,the population is 40,000. three years later the population is 38000. approximately how long does it take the population to decline from 40,000 to 20,000?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A certain population obeys the natural law of decay. at a certian time,the population is 40,000. three years later the population is 38000. approximately how long does it take the population to decline from 40,000 to 20,000?
-------------------
You have two points (0,40000) and (3,38000)
----
Assuming the decay is exponential, use the
model A(t) = ab^t
-----
Solve for a and b
------
Using (0,40000), solve for "a":
40,000 = ab^0
a = 40,000
----------------------
Now, A(t) = 40,000*b^t
Using (3,38000), solve for "b":
38000, = 40,000*b^3
19/20 = b^3
b = 0.983
===================
Equation:
A(t) = 40000*0.983^t
-------------------------
When does the population decay to 20,000?
20,000 = 40000*0.983^t
0.983^t = 0.5
t = log(0.5)/log(0.983)
t is approximately 40
Rounded up you would get 41 years
=========
Cheers,
Stan H.
RELATED QUESTIONS
A town has a population mean of 40,000 that is increasing at the rate of 5% each year.... (answered by mananth,ikleyn)
The size P of a certain insect population at time t (in days) obeys the function... (answered by mathmate)
The size P of a certain insect population at time t (in days) obeys the functions P (t) = (answered by Alan3354)
The population of a city is growing exponentially. Initially the population was 43,000... (answered by stanbon)
The size P of a certain insect population at time...t...(in days) obeys the function P... (answered by josgarithmetic)
A population of a colony of mosquitoes obeys the law of uninhibited growth.
a) If N (answered by rwm)
A sneaker shop pays its wholesaler $40 for a certian athletic shoe, and then sells it to... (answered by Alan3354)
If twice a certian number is increased by 3, the result is 8 less than threes time a... (answered by elima)
The size P of a small herbivore population at time t (in years) obeys the function P(t)... (answered by ewatrrr)