Solving Exponential Growth Problems

Solving Exponential Growth Problems-75
Examples of exponential decay are radioactive decay and population decrease.

C) What will the population of the city be in 2005? Since we are looking for the population, what variable are we seeking? The way the problem is worded, 1994 is what we call our initial year. Plugging in 0 for t and solving for A we get: When writing up the final answer, keep in mind that the problem said that the population was in thousands. Another way that we could have approached this problem was noting that the year was 1994, which is our initial year, so basically it was asking us for the initial population, which is Ao in the formula.

This happens to be the number in front of e which is 30 in this problem.

If we are looking for the number of grams of carbon-14 present, what variable do we need to find? What are we going to plug in for t in this problem?

Since t represents the number of years, it looks like we will be plugging in 10,000 for t.

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?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.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.The half-life of a given substance is the time required for half of that substance to decay or disintegrate.The diagram below shows exponential decay:: An artifact originally had 12 grams of carbon-14 present.The reason I showed you using the formula was to get you use to it.Just note that when it is the initial year, t is 0, so you will have e raised to the 0 power which means it will simplify to be 1 and you are left with whatever Ao is. Well, k = .0198026, so converting that to percent we get 1.98026% for our answer.Or you can use it to find out how long it would take to get to a certain population or value on your house.The diagram below shows exponential growth:: The exponential growth model describes the population of a city in the United States, in thousands, t years after 1994.


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