Question

Let F(s) 1.1s + 0.03s2 represent the stopping distance (in feet) of a car travelling at s miles per hour. Calculate F(60) and estimate the increase in stopping distance if speed is increased from 60 to 61. Compare your estimate with the actual increase. F(60) Estimated increase in stopping distance: Actual increase in stopping distance: feet feet feet The dollar cost of producing x bagels is C(a) 3000.25x 0.51000 Determine the cost of producing 3000 bagels. (Use decimal notation. Give your answer to three decimal places.) C(3000) dollar Estimate the cost of the 3001 st bagel. (Use decimal notation. Give your answer to three decimal places.) The cost of the 3001 st bagel is dollar Find the actual cost of the 3001 st bagel. (Use decimal notation. Give your answer to three decimal places.) The actual cost of the 3001 st bagel is dollar help (decimals) help (decimals) help (decimals)

Answer 1

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.

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) =
`(dF(s))/(ds)` = 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 (
`(x)/(1000)`)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.