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Answer:
F(60) = 3666 feet
Estimated Increase in Stopping Distance: 123.1 feet
Actual Increase in Stopping Distance: 122.1 feet
The cost of producing 3000 bagels is $1036.5
The Estimated cost of the 3001st bagel is $1036.736.
The actual cost of the 3001 st bagel is $1036.737.
Step-by-step explanation:
F(s) = 1.1s + s²
F(60) = 1.1(60) + (60)²
= 66 + 3600
F(60) = 3666 feet
To find the estimate increase in stopping distance, differentiate the function to get F'(s) and then find F'(61)
F'(s) = = 1.1 + 2s
F'(61) = 1.1 + 2(61)
F'(61) = 123.1 feet
If speed is increased from 60 to 61, we can find the actual increase by finding F(61) and then subtracting F(60) from it.
F(61) = 1.1(61) + (61)²
F(61) = 3788.1 feet
Increase = 3788.1 - 3666
Increase = 122.1 feet
F(60) = 3666 feet
Estimated Increase in Stopping Distance: 123.1 feet
Actual Increase in Stopping Distance: 122.1 feet
C(x) = 300 + 0.25x - 0.5 ()³
C(3000) = 300 + 0.25(3000) - 0.5 (3000/1000)³
= 300 + 750 - 13.5
C(3000) = $1036.5
The cost of producing 3000 bagels is $1036.5
To estimate the cost of the 3001st bagel, we need to differentiate the function and then find the increase in price at the 3001st bagel. The answer then needs to be added to C(3000). So,
C'(x) = 0.25 - 0.5*3 (x/1000)²/1000
C'(3001) = 0.25 - 0.5*3 (3001/1000)²/1000
C'(3001) = 0.236
C(3001) = C(3000) + C'(3001)
= 1036.5 + 0.236
C(3001) = $1036.736
The Estimated cost of the 3001st bagel is $1036.736.
C(3001) = 300 + 0.25(3001) - 0.5(3001/1000)³
= 300 + 750.25 - 13.5135
C(3001) = $1036.737
The actual cost of the 3001 st bagel is $1036.737.