Some quantities increase exponentially at a certain rate per year (e.g. deer populations; money compounded annually). Other quantities increase exponentially at a continuous rate (e.g. human populations; money compounded continuously).

a. Suppose an initial amount of 100 (deer or dollars, your choice) increases at an annual rate of 7.8%. How long will it take for the amount to double? Round to the nearest 0.01 year

b. How long would it take for the same initial amount to double if it increases at a continuous rate of 7.8%?

c. Which is longer, and by how much? Give your answer in years, and also convert this answer to months.

d. How would your answers change if you started with an initial amount of 1000?