Thread: Applications of exponential equations

I have two problems on my test review that I have no idea where to start.

1.) The population of Merchantville was 20,000 in 1990 and 25,000 in 1995. If exponential growth is assumed, find a model for the population growth and then use the model to determine the population in 2008.


2.) A sample of 500 grams of radioactive lead 210 decays to polonium 210 according to the function A(t)=500e^-.032(t), where t is in years. Find the amount of the sample remaining after half-life.

Thanks in advance!

1.) The population of Merchantville was 20,000 in 1990 and 25,000 in 1995. If exponential growth is assumed, find a model for the population growth and then use the model to determine the population in 2008.

Let A = initial amount
And B = final amount
And t = time in years

You can use
1) B = A*a^t
or 2) B = A*e^(kt)
to get the same answer.

A = 20,000
B = 25,000
t = 1995 -1990 = 5 yrs
So,
25,000 = 20,000a^5
5ln(a) = ln(25,000/20,000)
ln(a) = ln(25/20) /5 = 0.04462871
a = e^0.04462871 = 1.045639553

Hence,
B = A*(1.045639553)^t

So in 1998, say, based from 1995, where t = 3,
C = 25,000(1.045639553)^3 = 28,582 ---------------answer.


2.) A sample of 500 grams of radioactive lead 210 decays to polonium 210 according to the function A(t)=500e^-.032(t), where t is in years. Find the amount of the sample remaining after half-life.

Not very clear.
Does that mean the half-life of Lead 210, or of Polonium 210? Are those two materials the same in half-lives?