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Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

Applications Involving Exponential Models

Exponential functions are useful in modeling many physical phenomena, such as populations, interest rates, radioactive decay, and the amount of medicine in the bloodstream. An exponential model is of the form A = A0(b)t/c where we have:

  • A0 = the initial amount of whatever is being modelled.
  • t = elapsed time.
  • A = the amount at time, t.
  • b = the growth factor. Note that if b > 1, then we have exponential growth, and if 0< b < 1, then we have exponential decay.
  • c = time it takes for the growth factor b to occur.

Example: Suppose that the initial number of bacteria in a sample is 6000 and that the population triples every 2 hours. Set up the corresponding model for the number of bacteria as a function of time.


f(t) = 6000 ∙ 3t/2

Example: If a substance has a half-life of 18 years and we start with 27 mg, determine the appropriate model for how much of the substance we have at any given time.


f(t) = 27 ∙ (1/2)t/18

Once a model has been set up, known data can be substituted in and the resulting exponential equation can be solved for an unknown variable, which is often t, A, or A0.

Example 1:

Example 2:

Example 3: