Chapter 4: EXPONENTIAL FUNCTIONS Lesson 1: Representing Real-Life Situations Using Exponential Functions Activity 3 1. Suppose that a couple invested P 50 000.00 in an account when their child was born, to prepare for the child's college education. If the average interest rate is 4.4% compounded annually a. Give an exponential model for the situation b. Will the money be doubled by the time the child turns 18 years old? 2. You take out a P 20 000.00 loan at a 5% interest rate. If the interest is compounded annually a. Give an exponential model for the situation b. How much will you owe after 10 years? 3. Suppose that the half-life of a substance is 250 years. If there were initially 100g of the substance a. Give an exponential model for the situation b. How much will remain after 500 years? 4. A population starts with 1 000 individuals and triples every 80 years a. Give an exponential model for the situation b. What is the size of the population after 100 years? 5. P 10 000.00 is invested at 2% compounded annually. a. Give an exponential model for the situation b. What is the amount after 12 years? 6. The amount of money in peso is invested at P(t) = 10 000e 0.05t. How long will it take for initial investment to Round off your answer to the nearest year) a. Double the value b. Triple the value c. Quadruple the value 7. Robert invested P 30 000 after graduation. If the average interest rate is 5.8% compounded annually, a. Give an exponential model for the situation b. Will the money be doubled in 15 years? 8.At time t = 0, 500 bacteria are in the petri dish, and this amount triples every 15 days. a. Give an exponential model for the situation b. How many bacteria are in the dish after 40 days? 9. The half-life of a substance is 400 years. a. Give an exponential model for the situation b. How much will remain after 600 years if the initial amount was 200 grams? 10. The population of the Philippines can be approximated by the function P(x) = 20000000e 0.025x (0 S x s 40) where x is the number of years since 1955 (e.g x = 0 at 1955). Use this model to approximate the Philippine population during the years 1955, 1965, 1975, and 1985. Round off your answer to the nearest thousand 1955 (t = 0) 1965 (t = 10) 1975 (t = 20) 1985 (t = 30) 1 1. A barangay has 1 000 individuals and its population doubles every 60 years. Give an exponential model for the barangay. What is the barangay's population in 10 years? 12. A bank offers a 2% annual interest rate, compounded annually for a certain fund. Give an exponential model for a sum of P 10 000 invested under this scheme. How much money will there be in the account after 20 years? 13. The half-life of a radioactive substance is 1200 years. If the initial amount of the substance is 300 grams, give an exponential model for the amount remaining after t years. What amount of substance remains after 1 000 years