Question 403773: 2. The table shows the number of squirrels in a particular forest t years after a forest fire.
Number of Squirrels
Years Squirrels
.0............30
.1............60
.2...........120
.3...........240
.4...........480
.5...........960
Write a function to model the situation. Explain what each number represents.
2. In a particular region of a national park, there are currently 330 deer, and the population is increasing at an annual rate of 11%.
a. Write an exponential function to model the deer population.
b. Explain what each value in the model represents.
c. Predict the number of deer that will be in the region after five years. Show your work.
If you can answer all that would be great thanks!!!
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! This is a bit much to ask in a single post. So I am going to solve the harder problem, the second one. If my explanation of the second problem does not give you a clue about how to do the first problem, then repost the first problem by itself.
Both of these problems are exponential growth problems. They are exponential growth problems because the amount changes by the same factor for each unit of time. (Units of time can be seconds, minutes, hours, etc. In both your problems the units of time are years so I will use the words "years" instead of the more general "units of time".) In other words, with exponential growth you take one year's amount and multiply it by some constant factor to get the next years amount.
In your first problem you will find that if you take the numbers of squirrels from any two consecutive years and divide them (the newer amount divided by the older amount) you end up with the same number no matter what consecutive years you use! This is what tells you that it is an exponential growth function.
In the second problem you are told that the growth is 17% for each year. This pretty much comes right out and tells you that it is an exponential growth function.
The general form for exponential growth (or decline) functions is:
 where
A = an amount. (In the first problem it would be the number of squirrels. In the second problem it would be the number of deer.)
A[0] = the initial amount. IOW, the amount when t = 0. You get to decide what time t=0 represents. In the first problem your years are already numbered so it is obvious when t = 0. In the second problem, we'll decide that t = 0 means the time when there were 330 deer.
r = rate of change. For exponential growth  . For exponential decline,  .
t = the number of units of time (years in both your problems) since the t = 0 time.
To find the equations for both problems, you must figure out what  and "r" are and put those numbers into the general form. For the second problem, since we decided that the t=0 time was when there were 330 deer, = 330.
The hard part is the "r". By what factor is the number of deer increasing? We are told that the growth is 17%. At first thought you might think that the growth factor is 17%. But there are two things wrong with that:- You just about never do any calculations with percents. You must change the percent into a decimal or fraction and do the calculations with the decimal or fraction.
- Even if you change 17% to 0.17, the growth factor is not 0.17. Multiplying by 0.17 makes a number smaller, not larger.
When something grows by 17% it means one year's amount is 17% more than the previous years. In other words, you get one year's amount by taking the whole amount from the previous year and add 17% of that amount. This makes the growth factor:
1 + 0.17 or 1.17
The "1" is for the "whole" and the "+ 0.17" is for the "17% more". So for the second problem:
r = 1.17
We are now ready to write an equation for the second problem. Insert 330 for and 1.17 for "r" we get:
To find the number of deer 5 years from now we use a 5 for t since the t=0 time is now:
I'll leave it up to you to finish. Some reminders and suggestions:- Use the order of operations (aka PEMDAS) to simplify the right side.
- You will probably want to use a calculator.
- Your answer will probably not be a whole number. Since A is a number of deer and since fractions of a deer do not make sense, round off your answer to the nearest whole number.
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