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Problem Number 7

If a(n) = a(n-1) + 9, with a(0) = -9, then what is the value of a( 310)?

Compounding $1000 initial principle continuously, for 1 year, at 100% annual interest:

If we compound interest annually at annual rate 8% then if we start with $1000, how much do we have after 5 years?

Compounding annually we multiply our principle by 1.08 every year, so we end up with $1000 * 1.08^5 = $1469.32.

If we compound interest monthly at annual rate 8% then if we start with $1000, how much do we have after 5 years?

Compounding monthly we multiply our principle by 1 + .08 / 12 = 1.006667 every month.  In 5 years we do this 5 * 12 times, so we end up with $1000 * 1.006667^(5 * 12) = $1487.90.

If we compound interest continuously at annual rate 8% then if we start with $1000, how much do we have after 5 years?

Continuous compounding gives us principle function P(t) = $1000 * e^(.08 t).

For t = 5 we have principle

The most basic exponential function forms are

The generalized forms for horizontal asymptote zero are

Using the form y = A * b^x, assume that y = 20 when x = 5 and y = 30 when x = 12.  Find the values of the parameters A and b.