Calculus question?

Question

Okay so some of you will probably think this stuff is easy but i just don't get it. If someone could please give me step-by-step instructions on how to figure out one/both of the following questions:

1. If john invests $2300 in a savings account with a 6% interest rate compounded annually, how long will it take until his the account has a ablance of $4150?

2. Determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25% compounded annually.


And on a side note, I have the equation A=P(1+r/n)^nt - if i fill in the numbers that I know, how do I solve it if the variable is in the exponent?

here's two more:

3. determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25% compunded monthly.

4. determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25% compunded continuously.

Answer 1

1) 2300(1.06)^n = 4150. So 1.06^n = 4150/2300 = 1.804, and n ln(1.06) = ln(1.804), so n = ln(1.804)/ln(1.06) = 10.13 years

2) 2 = 1.0625^n, and n*ln(1.0625) =ln(2), or n = ln(2)/ln(1.0625) = 11.43 years

Answer 2

i could say shape is a factor of engineering meaning that a reliable draw close on math is important, pre-cal is is like algebra to the subsequent point with the Pi chart and understanding approximately radians and perspective measures (which seems significant) yet Calculus is the learn of derivatives, (the slope of a line at a definite factor) form of pointless no be counted what container of workd your going to, in case you inquire from me.

Answer 3

4150 = 2300 ( 1+0.06) ^t ( t in years
log (4150/2300) =t *log(1.06)
so t= 10 years approx
2) 2C = C( 1.0625)^t so t= log2/log(1.0625)
In the examples you´ll see that the solution is in taking log