A bank account that accrues continuously compounded interest grows in value at a rate pro- portional to its current value.

Question

The current value is modeled by the exponential equation y = y0e^rt, where r is the annual interest rate, t is time in years, and y0 is the initial value of the account. Suppose after 2 years, the account held $10,000 and after 5 years, the account

held $12,000.

(b) Use this to determine when the account will reach a value of $15,000.

(c) Suppose $10,000 was the “initial” value and $12,000 was the value after 3 years. Find r and the value of the account 2 years BEFORE the “initial” time. In a print statement, explain what you notice when comparing these answers to part (a).

Answer 1

Given your formula, you can set up two equations, one for your amount at two years (10,000) and one for your amount at 5 years (12,000):

y = y₀e^rt

12,000 = y₀e^5r

10,000 = y₀e^2r

Now you have two equations and two unknowns (r and y₀), so you can solve for both.

Part C is similar, but now y₀ = 10,000 and y(t=3) = 12,000.