1. Do Now How long would it take for an initial deposit of $1000 to grow into $1500 if you deposit it into an account that earns 4% interest compounded monthly? Find the future value of an investment of $5200 deposited into an account that earns 2.5% interest compounded quarterly. Solve for x:

2. Do Now Solutions: How long would it take for an initial deposit of $1000 to grow into $1500 if you deposit it into an account that earns 4% interest compounded monthly? Find the future value of an investment of $5200 deposited into an account that earns 2.5% interest compounded quarterly.

3. Solutions, contd: Solve for x:

4. CH 4 TEST WEDNESDAY Tomorrow: Review properties, equations

5. Form: How long will it take for the money in an account that is compounded continuously at 3% to quadruple?

6. Example: Radioactive decay* Strategy: Use initial amount and data point to solve for constant k. Then use equation to answer question. If 800 mg of a radioactive substance are present initially and 2.5 years later, only 400 mg remain, how much of the substance will be present after 4 years?

7. Example: Radioactive decay* Strategy: Use initial amount and data point to solve for constant k. Then use equation to answer question. If 2 g of a radioactive substance are present initially and 2 years later, only.25 g remain, how much of the substance will be present after 6 years?

8. Example: Carbon dating* Carbon 14, or radiocarbon, is a radioactive form of carbon that is found in all living things. It begins to disintegrate after the plant or animal dies Scientists can measure the age of the plant or animal after its death by measuring the amount of radiocarbon in the dead object and comparing it to living things Technique called carbon dating

9. Example: Carbon dating* The amount of radiocarbon present after t years is given by: Find the half-life. What does this mean in the context of the problem?

10. Example: Carbon dating* Suppose the skeleton of a woman who lived in the Classical Greek period was discovered in 2005. carbon 14 testing at that time determined that the skeleton contained ¾ of the carbon 14 of a living woman of the same size. Estimate the year in which the Greek woman died.

11. Modeling- types of applications 8 options, you choose 5: Compound interest Continuous interest Population growth or decay (strategy: data points) Carbon dating () Radioactive decay/ half life