The expression models the balance, in thousands of dollars, of an account years after the account was opened.

1. What is the account balance:
   1. when the account is opened?
   2. after 1 year?
   3. after 2 years?
2. Based on the expression, what is the continuous rate of growth offered for the account?
3. Diego says that the expression represents the time, in years, when the account will have 5 thousand dollars. Do you agree? Explain your reasoning.
4. Suppose you opened this account at the beginning of this year. Assume that you deposit no additional money and withdraw nothing from the account. Will the account balance reach $1,000,000 and make you a millionaire by the time you reach retirement? Show your reasoning.

A population of crickets under certain conditions can be modeled by a function defined by , where is the number of weeks since the population was first measured.

1. Explain why solving the equation gives the number of weeks it takes for the cricket population to double.
2. How many weeks does it take for the cricket population to double? Show your reasoning.
3. Use graphing technology to graph and   on the same axes. Explain why we can use the intersection of the two graphs to estimate when the cricket population will reach 100,000.