A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer.
Hint: Use the formula, f(x) = P(1 + r)^x
a. f(x) = 2,000(0.94)x, 952 square kilometers
b. f(x) = 2,000(1.06)x, 4,204 square kilometers
c. f(x) = 2,000(0.06)x, 1,239 square kilometers
d. f(x) = 2,000(0.94)x, 1,432 square kilometers
To find the function that represents the area of the forest each year, we can use the formula f(x) = P(1 + r)^x, where P is the initial area, r is the rate of decrease (in decimal form), and x is the number of years.
In this case, the initial area is 2,000 square kilometers, and the rate of decrease is 6%, or 0.06. Plugging these values into the formula, we get the function:
f(x) = 2,000(1 - 0.06)^x
Simplifying this gives us:
f(x) = 2,000(0.94)^x
Now, to find the remaining area after 12 years, we substitute x=12 into the function:
f(12) = 2,000(0.94)^12
Calculating this using a calculator, we find that f(12) is approximately 1,432 square kilometers.
Therefore, the correct answer is d. f(x) = 2,000(0.94)^x, 1,432 square kilometers.
i think f(x) = 2,000(0.94)^x, 952 square kilometers is the answer
If it is a decrease, r is negative.
In the proposed answers, the variable x is an exponent, so it should be written:
A. f(x)=2000(0.94)^x,...
and so on.
Which do you think is the right answer?
Tony, help is to give you hints or explanations to lead you to a solution.
Giving answers could be help for someone who wants to understand, and detrimental for someone who does not.
The help I gave above should help you eliminate two of the choices. If you need more information to distinguish between the remaining choices, you're welcome to express your wish.
Most students at this level can usually take out the calculator and evaluate the functions and see if they match the second answer of each choice. You can do the same to distinguish between the two remaining choices.
This is all the techniques you need to find the correct answer for this question. Since he same can be applied to similar problems in the future, I hope you have learned something from this problem.
A certain area of forest is populated by two species of animal, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as F1 and F2. For one year, each member of species A requires 1 unit of F1 and 0.5 unit of F2. Each member of species B requires 0.2 unit of F1 and 1 unit of F2. The forest can normally supply at most 600 units of F1 and 525 units of F2 per year. What is the maximum total number of these animals that the forest can support?
MathMate -
yes - the answers all have x as the exponent which should be ^.....
But regardless of that - you have not helped me in solution of this word problem... Can you assist or not ? And why would you ask me which answer is correct. IF I was able to come to that conclusion _ I would not be here asking for assistance.
Baloney! Many of our students have a couple ideas about the right answer, but post the question just to make sure.
If you have no ideas, then maybe you should restudy your lessons.