It has been found that a worker new to the operation of a certain task on the assembly line will produce P(t) items on day t, where P(t) = 25- 25 e0.5t. How many items will be produced on the 1st day, and what is the maximum number of items, according to the function, the worker can produce? ... The worker will produce items on the first day. (Round to the nearest whole number.)

It has been found that a worker new to the operation of a certain task on the assembly line will produce P(t) items on day t, where P(t) = 25- 25 e0.5t. How many items will be produced on the 1st day, and what is the maximum number of items, according to the function, the worker can produce? ... The worker will produce items on the first day. (Round to the nearest whole number.)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

It has been found that a worker new to the operation of a certain task on the assembly line will produce P(t) items on day t, where P(t) = 25 - 25 e0.5t.
How many items will be produced on the 1st day, and what is the maximum number of items, according to the function, the worker can produce?
The worker will produce items on the first day.
(Round to the nearest whole number.)
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Expert Solution

Step 1

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the given function is

$P\left(t\right)=25-25e^{-0.5t}$

take t=1 for the first day

$P\left(1\right)=25-25e^{-0.5\cdot 1}$

$P\left(1\right)=25-25e^{-0.5}$

$P\left(1\right)= 25-25\cdot 0.60653$

$P\left(1\right)= 25-15.1632664$

$P\left(1\right)= 9.83673$

$P(1)\approx 10$

the worker will produce ${\color{Red} 10 }$ items on the first day.

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