Solving Exponential Growth Problems

two function formulas were used to easily illustrate the concepts of growth and decay in applied situations.

If a quantity grows by a fixed percent at regular intervals, the pattern can be depicted by these functions..

We will still be using the same formula we did to answer the questions above, we will just be using it to find a different variable.

Plugging in 60 for A and solving for t we get: Since we are looking for when, what variable do we need to find? What are we going to plug in for A in this problem? Plugging 200000 for A in the model we get: t is the amount of time that has past.

As mentioned above, in the general growth formula, k is a constant that represents the growth rate. Since we are looking for the population, what variable are we finding? What are we going to plug in for t in this problem?

Our initial year is 1994, and since t represents years after 1994, we can get t from 2005 - 1994, which would be 11.Examples of exponential decay are radioactive decay and population decrease.The information found can help predict what the half-life of a radioactive material is or what the population will be for a city or colony in the future.Plugging in 10000 for t and solving for A we get: : A certain radioactive isotope element decays exponentially according to the model , where A is the number of grams of the isotope at the end of t days and Ao is the number of grams present initially. If we are looking for the half-life of this isotope, what variable are we seeking? It looks like we don’t have any values to plug into A or Ao.However, the problem did say that we were interested in the HALF-life, which would mean ½ of the initial amount (Ao) would be present at the end (A) of that time. Replacing A with .5 Ao and solving for t we get: : Prehistoric cave paintings were discovered in a cave in Egypt. Using the exponential decay model for carbon-14, , estimate the age of the paintings.Use this model to solve the following: A) What was the population of the city in 1994?B) By what % is the population of the city increasing each year?Since we are looking for the age of the paintings, what variable are we looking for? It looks like we don’t have any values to plug into A or Ao.However, the problem did say that the paintings that were found contained 20% of the original carbon-14.Plugging in 11 for t and solving for A we get: Looks like we have a little twist here.Now we are given the population and we need to first find t to find out how many years after 1994 we are talking about and then convert that knowledge into the actual year.

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