Question

A factory produces bicycles at a rate of 95 + 588t2 – 14t bicycles per week (t in weeks). How many bicycles were produced from the beginning of week 2 to the end of week 3? (Give your answer as a whole or exact number.) number of bicycles:

Answer 1

To find the number of bicycles produced from the beginning of week 2 to the end of week 3, calculate the total number of bicycles produced during these two weeks. Subtract the number of bicycles produced at the beginning of week 2 from the number of bicycles produced at the end of week 3.

Step-by-step explanation:

To find the number of bicycles produced from the beginning of week 2 to the end of week 3, we need to calculate the total number of bicycles produced during these two weeks.

Let's first find the number of bicycles produced at the beginning of week 2:

Week 2: t = 2

Bicycles produced at the beginning of week 2 = 95 + 588(2^2) - 14(2)

= 95 + 588(4) - 14(2)

= 95 + 2352 - 28

= 2419

Next, let's find the number of bicycles produced at the end of week 3:

Week 3: t = 3

Bicycles produced at the end of week 3 = 95 + 588(3^2) - 14(3)

= 95 + 588(9) - 14(3)

= 95 + 5292 - 42

= 5345

Now, to calculate the total number of bicycles produced from the beginning of week 2 to the end of week 3, we subtract the number of bicycles produced at the beginning of week 2 from the number of bicycles produced at the end of week 3:

Total number of bicycles produced = 5345 - 2419

= 2926

Therefore, the number of bicycles produced from the beginning of week 2 to the end of week 3 is 2926.

Answer 2

The number of bicycles produced from the beginning of week 2 to the end of week 3 is 2926 bicycles

Step-by-step explanation:

To find the number of bicycles produced from the beginning of week 2 to the end of week 3, we need to calculate the total production during that time period.

First, let's find the production at the beginning of week 2. We substitute t=2 into the production function:

Production at the beginning of week 2 = 95 + 588(2^2) - 14(2) bicycles per week = 95 + 588(4) - 14(2) bicycles per week = 95 + 2352 - 28 bicycles per week = 2419 bicycles per week

Next, let's find the production at the end of week 3. We substitute t=3 into the production function:

Production at the end of week 3 = 95 + 588(3^2) - 14(3) bicycles per week = 95 + 588(9) - 14(3) bicycles per week = 95 + 5292 - 42 bicycles per week = 5345 bicycles per week

To calculate the total production during this time period, we subtract the production at the beginning of week 2 from the production at the end of week 3:

Total production from the beginning of week 2 to the end of week 3 = 5345 bicycles per week - 2419 bicycles per week = 2926 bicycles