Mia invested $640 in an account paying an interest rate of 6.7% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $940?

The formula for compounding interest is A=Pe^rt where A = the Amount in the account P = the Principal amount e = a mathematical constant (this is automatically programmed in your scientific calculator) ^ (this means that it is raised to) r = rate of interest t = time in years
For this problem, the formula would look like this
940 = 640e ^ (.067t)
We need to divide both sides by 640 to get e by itself so we get the fraction 47/32

47/32 = e ^ (.067t)
Now we need to get rid of the e by taking the natural log or ln (on the calculator) on both sides

(ln (47/32)) = .067t
Now we need to divide both sides by .067 to figure out t or the amount of time it will take for the account to reach $940

(ln (47/32)) ➗(.067) = t

So, after calculating this on the calculator, t = 5.737 years and if you round to the nearest year,
t = 6 years