# Thread: Exponential Growth and Decay Problems

1. ## Exponential Growth and Decay Problems

The Problems:
1. Use separation of variables to solve the initial value of the problem, include domain too: dy/dx=cos^2 y. (cosine to the second, the y isn't part of the exponent.) when y=0 and x=0

2. The rules state that it takes about 70/i or 72/i years for money to double at i percent, compounded continuously, using whichever of 70 or 72 is easier to divide by i.
a) Show that it takes t=(ln2)/r years for money to double if it is invested at annual rate r (indecimal form) compounded continuously.
b) Explain why these two rules of thumb for mental computation are reasonable.
c) Use rules to estimate how long it takes to double money at 5% compound continously.
d) Then make a rule estimating the amount of years needed to triple your money.

so for the first one, i move the x variables to one side and the y to the other: dy/cos^2 (y)=dx
Then i find the integral of both sides: x=ln lcos^2 (y)l ? i know i have that integral wrong, I need help with that.

The second one, I don't understand what the problem is asking really.
Would be helpful if you explained everything you do to get the answer, thank you.

The Problems:
1. Use separation of variables to solve the initial value of the problem, include domain too: dy/dx=cos^2 y. (cosine to the second, the y isn't part of the exponent.) when y=0 and x=0

so for the first one, i move the x variables to one side and the y to the other: dy/cos^2 (y)=dx
Then i find the integral of both sides: x=ln lcos^2 (y)l ? i know i have that integral wrong, I need help with that.
$\frac{dy}{\cos^2{y}} = dx$

$\sec^2{y} \, dy = dx$

now integrate.