Question

2x = 400 9

Answer 1

Start with
\[\large A=Pe^{rt}\]

Answer 2

Not quite. There was an error in your solving.

Answer 3

2=e^rt
ln 2 = rt

Answer 4

How did you get that?

Answer 5

I don't think simple interest applies here. That wouldn't require logarithms.
7.2 percent is close to what I got. Did you round off anywhere along the way?

Answer 6

7.2 is a good approximation using the rule of 72, but it is less precise than using the exponential formula.

Answer 7

Not using logarithms. How did you get the 7.2? Did you use the t=72/r approximation?

Answer 8

Ok, that's good, that gives a good estimate, but to be more precise, use the exponential.
\[\large A=Pe^{rt}\]
A=8000, P=4000, t=10
A/P=2
\[\large \rightarrow 2=e^{10r}\]

Answer 9

Taking the natural log of both sides:
\[\large ln(2) = 10r \rightarrow r=\frac{ln(2)}{10}\]

Answer 10

No, P=4000

Answer 11

No, you need to solve 2=e^rt, which has been solved to get r=ln(2)/10.
You need to evaluate ln(2)/10 to get a value for r.

Answer 12

That's better. (or even 6.93%) See how that is close to the 7.2% estimate?