Expert: Sherman D. - 7/30/2007

Question
I have 3 quick questions I was wondering if u could explain to me.
1.)If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance?

2.)What is the difference between exponential growth and logistic growth?

3.) Would one prefer that their salary be modeled exponentially or logarithmically? Why?

Thanks in advance!

Answer
1.)
y = 4000(1 + .03)^x
y = 2000(1 + .05)^x

4000(1.03)^x = 2000(1.05)^x
2(1.03)^x = (1.05)^x
((1.05)^x/(1.03)^x) = 2
(1.05/1.03)^x = 2
x(1.05/1.03) = ln(2)
x = ln(2)/(1.05/1.03)
x = (1.03ln(2))/(1.05)
x = about .6799

But when i type that it, it doesn't work. So i graphed it and i found out that the 2 graphs never meet.

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2.)
exponential growth is a growth that grows at a faster rate as the value of x increases.
logarithmic growth is a growth that grows gradually(little by little) as the value of x increases.

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3.)
Exponentially. Same reason above. Their salary would become larger at a quicker rate than if it were logarithmicly modeled.