Suppose you want \$2000 in 3 years. The interest rate for a savings account is 2.8% compounded annually. The money, \( P \) dollars, you must invest now is given by \( P = 2000(1.028)^{-3} \). How much must you invest now to have \$2000 in 3 years?
Apply a compound interest formula with a negative exponent.
A colony of Fruit Flies triples every 30 minutes. If there are 19,683 Fruit Flies now, how many were present 2 hours ago?
Exponential growth application.
Determine the value of \( n \) that makes \( \left(\frac{5}{4}\right)^n = \frac{64}{125} \).
A colony of Fruit Flies doubles every 10 minutes. If there are 19,683 Fruit Flies now, how many were present 1 hour ago?
Exponential growth application.
The remaining mass of radioactive iodine-131 is given by the formula \( M = M_0(2)^{-t/8} \), where \( M \) is the remaining mass in grams, \( M_0 \) is the initial mass in grams, and \( t \) is the time in days. If the initial amount of iodine-131 is 726 grams, how much is left after 8 days?
Short answer. Use exponential decay.
