Assignment 10

1. Consider investing $1 at a rate r% /year. How much do you have after T years if the interest is compounded annually? Daily? N times per year? Write this amount as (…)^rt. Plug in some large values for N. What happens?

2. A radioactive substance has a half-life of 370 hours. Write a formula for the amount remaining after t hours, assuming you started with 100 grams. Now rewrite your function in terms of the exponential function e^t.

3. Why don’t we consider exponentials a^x with a<0?

4. Consider three graphs: 2^x, 2^x shifted by 1 to the right, and 2^x compressed vertically by ½. Compare. Explain.

5. E. Coli can double every 20 minutes under ideal conditions. How many would you have after one day starting with a single bacterium? 2 days? If each bacterium weighs ~4*10^-13 grams, what would the mass be after 2 days?