C) Beth invests $2000 at a rate of 2% per year compound interest.
Calculate the minimum number of complete years it takes for the value
of Beth's investment to increase from $2000 to more than $2500.

Step-by-step explanation:

We'll first find out how long it takes for the account to have 2500 in it, then we'll add a year (we'll check ourselves anyway, just to be sure!) This is an exponential growth problem of the form

since the compounding is only done once a year. Filling in:

Begin by dividing both sides by 2000 to get

In order to get that t down from its current position in the equation, we will take the natural log of both sides. This allows us to pull the t down and put it out front like this:

ln(1.25) = t ln(1.02)  Now divid both sides by ln(1.02) and you will see that

t = 11 years. At 11 years (rounded), the account will have

= 2486.75 and after 12 years:

= 2536.48

t = 12 works!