Leonardo, Shane Karla W
Easy Difficulty
Growth and Decay
1. The half-life of a radioactive substance is 2 days. Find the time required for a given amount
1
of the material to decay to 10 of its original mass
Ans:
𝑇=
2𝑙𝑛10
𝑙𝑛2
𝑑𝑎𝑦𝑠 𝑜𝑟 6.644 𝑑𝑎𝑦𝑠
Alon, Justine Dominique M.
Medium Difficulty
Compound Interest
1. A person deposits $25,000 in a bank that pays 5% per year interest, compounded
continuously. The person continuously withdraws from the account at the rate of $750 per
year. Find 𝑃(𝑡), the value of the account at time 𝑡 after the initial deposit.
𝑡
Ans: 𝑃(𝑡) = 1500 + 1000𝑒 20
Ramirez, Jovaci Andrew L.
Hard Difficulty
Newton’s Law of Cooling
1. A thermometer initially reading 212°F is placed in a room where the temperature is 70°F.
After 2 minutes the thermometer reads 125°F.
(a) What does the thermometer read after 4 minutes?
(b) When will the thermometer read 72°F?
(c) When will the thermometer read 69°F?
Ans: 𝑎. ) 𝑇(4) = 91.30°F
𝑏. ) 𝑡 = 8.989 𝑚𝑖𝑛𝑠
c.) Since T > 70 for all t > 0, therefore, the thermometer will
never read 69°F.