If 8000 dollars is invested in a bank account at an interest rate of 5% per year, compounded continuously?
How many years will it take for your balance to reach 20000 dollars?

Question

anonymous · Answer

y=Ae^(kt)

anonymous · Answer

k=0.05 , the "growth constant" , which is 5%

anonymous · Answer

The initial value is 8000 , so A=8000
\

anonymous · Answer

y=8000e^(0.05t)

anonymous · Answer

20 000 = 8000e^(0.05t)

Solve for t.

anonymous · Answer

e^(0.05t) = (20/8)

0.05t = ln(20/8)

t= (1/0.05) ln(20/8)

anonymous · Answer

$$t= \frac{1}{0.05} \ln(\frac{20}{8})$$ and that is in years.

I don't have a calculator but you can sub into a calculator to get the actual value.

anonymous · Answer

" compounded continuously" means it is an exponential growth,

anonymous · Answer

thank you very much