A land conservation trust has an initial area of 720 acres. The growth plan will add 84 acres of land to the trust each year. If a function is written in the form f(x) = ax + b, where f(x) represents the number of acres of land in the trust and x repre-sents the number of months that have passed, what is the value of x when f(x) = 1, 126
A 4.83
B 13.4
C 58
D 406
The correct answer and explanation is:
To solve this problem, we first need to identify the values for the function in the form f(x)=ax+bf(x) = ax + b. Here, f(x)f(x) represents the number of acres of land in the trust, and xx represents the number of months that have passed.
Step 1: Understanding the problem.
- The trust starts with an initial area of 720 acres. This means when x=0x = 0 (the starting point), the number of acres is 720. Therefore, b=720b = 720.
- Each year, the trust adds 84 acres of land. Since there are 12 months in a year, this means the trust adds 8412=7\frac{84}{12} = 7 acres per month. Therefore, a=7a = 7.
Thus, the function can be written as: f(x)=7x+720f(x) = 7x + 720
Step 2: Solve for xx when f(x)=1,126f(x) = 1,126.
We are asked to find xx when the number of acres reaches 1,126. So, substitute f(x)=1,126f(x) = 1,126 into the equation: 1,126=7x+7201,126 = 7x + 720
Step 3: Solve for xx.
First, subtract 720 from both sides: 1,126−720=7×1,126 – 720 = 7x 406=7×406 = 7x
Now, divide both sides by 7: x=4067=58x = \frac{406}{7} = 58
Conclusion:
The value of xx when the trust has 1,126 acres is 58 months.
Thus, the correct answer is C: 58.