Final answer:
The cost of producing 10 ounces of gold from a new gold mine is $55.
Step-by-step explanation:
The cost of producing x ounces of gold from a new gold mine can be expressed as a function c = f(x) dollars. To find the cost of producing 10 ounces of gold, substitute x = 10 into the function. Let's assume the cost function is linear, so we can use the concept of slope and y-intercept. If the cost per ounce decreases by a constant amount for each additional ounce, we can say that the function is in the form c = mx + b, where m represents the slope and b represents the y-intercept.
Given the information, we can calculate the value of m by using the equation:
m = (f(x2) - f(x1)) / (x2 - x1)
Let's assume the cost for producing 1 ounce of gold is $100, and the cost for producing 2 ounces of gold is $95. Substituting these values into the equation, we get:
m = (95 - 100) / (2 - 1) = -5
Now that we have the value of m, we can find the y-intercept by using the equation:
b = f(x1) - mx1
Substituting the values of x1 = 1, f(x1) = 100, and m = -5 into the equation, we get:
b = 100 - (-5)(1) = 105
Now that we have the values of m and b, we can plug in x = 10 into the function:
c = mx + b = -5(10) + 105 = 55
Therefore, the cost of producing 10 ounces of gold is $55.