The Trouble With Tribbles or ...

more about exponential modeling

tribbles by flickr user tr67

Example 1: A colony of bacteria doubles every 6 days. If there were 3000 bacteria to begin with how many bacteria will there be in 15 days?

The Trouble with Tribbles

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Example 2: The mass (in grams) of radioactive material in a sample is given by:

where t is measured in years.

(a) Find the half-life of this radioactive substance.

(b) Create a model using the half-life you found in (a). How much of a 10 gram sample of the material will remain after 40 years?

Example 2: The mass (in grams) of radioactive material in a sample is given by:

where t is measured in years.

(a) Find the half-life of this radioactive substance.

(b) Create a model using the half-life you found in (a). How much of a 10 gram sample of the material will remain after 40 years?

Example 2: The mass (in grams) of radioactive material in a sample is given by:

where t is measured in years.

(a) Find the half-life of this radioactive substance.

(b) Create a model using the half-life you found in (a). How much of a 10 gram sample of the material will remain after 40 years?

In 1999, the population of Winnipeg was 630 700, and was increasing at the rate of 0.54% per year.

(e) Write the equation in part (a) as an exponential function with base e.

(d) Write the equation in part (a) as an exponential function with base 2.

(c) Calculate when the population will reach 1 million.

(b) Calculate how many years it would take for the population to double.

(a) Write an equation to represent the population of Winnipeg, P, as a function of the number of years, y, since 1999.