Answer:
5
Step-by-step explanation:
I did the marh
It would take 10.7 years.
The formula for continuously compounded interest is:
![A=Pe^{rt}](https://tex.z-dn.net/?f=A%3DPe%5E%7Brt%7D)
where P is the principal, r is the interest rate as a decimal number, and t is the number of years.
Using our information we have:
![A=Pe^{0.065t}](https://tex.z-dn.net/?f=A%3DPe%5E%7B0.065t%7D)
We want to know when it will double the principal; therefore we substitute 2P for A and solve for t:
![2P=Pe^{0.065t}](https://tex.z-dn.net/?f=2P%3DPe%5E%7B0.065t%7D)
Divide both sides by P:
![\frac{2P}{P}=\frac{Pe^{0.065t}}{P} \\ \\2=e^{0.065t}](https://tex.z-dn.net/?f=%5Cfrac%7B2P%7D%7BP%7D%3D%5Cfrac%7BPe%5E%7B0.065t%7D%7D%7BP%7D%0A%5C%5C%0A%5C%5C2%3De%5E%7B0.065t%7D)
Take the natural log, ln, of each side to "undo" e:
![\ln{2}=\ln{e^{0.065t}} \\ \\0.6931471806=0.065t](https://tex.z-dn.net/?f=%5Cln%7B2%7D%3D%5Cln%7Be%5E%7B0.065t%7D%7D%0A%5C%5C%0A%5C%5C0.6931471806%3D0.065t)
Divide both sides by 0.065:
This line is given to us in standard form,
![Ax+By=C](https://tex.z-dn.net/?f=Ax%2BBy%3DC)
, but it's easiest to see the slope when we convert to slope-intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
, where m is the slope.
We are going to solve for y.
![5x+y=15\\5x-5x+y=-5x+15\\y=-5x+15\\m=-5](https://tex.z-dn.net/?f=5x%2By%3D15%5C%5C5x-5x%2By%3D-5x%2B15%5C%5Cy%3D-5x%2B15%5C%5Cm%3D-5)
The slope is the coefficient of the x-term, –5.
The answer is 9
You divide by -2 on both sides leaving you with X=9
Make the percent into a decimal.