Please Help! Geometry!
1 answer:
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Answer:
a) Y(x) = {900, x≤30; 900-40(x-30), x>30}
b) T(x) = {900x, x≤30; 2100x-40x², x>30}
c) dT/dx = {900, x≤30; 2100-80x, x>30}
Step-by-step explanation:
a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.
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b) The yield per acre is the product of the number of trees and the yield per tree:
T(x) = x·Y(x)
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c) The derivative is ...
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The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.
So for this problem, we will be using the exponential equation format, which is y = ab^x. The a variable is the initial value, and the b variable is the growth/decay.
Since our touchscreen starts off at a value of 1200, that will be our a variable.
Since the touchscreen is decaying in value by 25%, subtract 0.25 (25% in decimal form) from 1 to get 0.75. 0.75 is going to be your b variable.
In this case, time is our independent variable. Since we want to know the value 3 years from now, 3 is the x variable.
Using our info above, we can solve for y, which is the cost after x years.
In context, after 3 years the touchscreen will only be worth $506.