SOLUTION: if $350 is deposited in an account paying 2% annual interest, compunded continuously, how long will it take for the account to increase to $1500? A=Pe^rt 1500=350e^.02(t)

Question 193252: if $350 is deposited in an account paying 2% annual interest, compunded continuously, how long will it take for the account to increase to $1500?

A=Pe^rt
1500=350e^.02(t)
then im lost...
Found 2 solutions by MathGuyJoe, jim_thompson5910:
Answer by MathGuyJoe(20) (Show Source): You can put this solution on YOUR website!
To Solve:
You must first isolate the e^x component -- so divide both sides by 350:

Simplifying gives you:

Next, take the natural log (ln) of both sides:

Now, use the power rule to simplify the right side:

Since , you're left with:

Divide both sides by .02 to get:

So t = 72.76 years

Hope this helps.

~ Joe
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Plug in A=1500, P=350, and r=0.02

Divide both sides by 350.

Divide

Take the natural log of both sides (to eliminate the base "e")

Evaluate the natural log of 4.2857

Divide both sides by 0.02

Divide

Rearrange the equation

So it will take approximately 72.765 years for $350 to grow into $1,500.
RELATED QUESTIONS
If $500 is deposited in an account paying 8.6% annual interest, compounded continuously,... (answered by Fombitz)
If $1,500 is deposited in a savings account paying 5% compounded quarterly, how long will (answered by stanbon)
if $500 is deposited in an account paying 8.7% annual interest, compounded continuously,... (answered by Boreal,MathTherapy,greenestamps)
If $ 500 is decompressed in an account paying 8.5% annual interest, compounded... (answered by ikleyn,ankor@dixie-net.com)
If $500 is deposited in an account paying 8.7% annual interest, compounded continuously,... (answered by MathTherapy)
I need help with this question If 500 is deposited in an account paying 8.5% annual... (answered by stanbon)
Exponential and Logarithmic Functions. Compound Interest. If $500 is deposited in an... (answered by stanbon,venugopalramana)
$300 is deposited into an account that pays 8.2% annual interest that is compounded... (answered by stanbon)
Suppose you deposit $275 in an account paying 4% annual interest, compounded... (answered by Theo)