The approximate rate of change in the number of design patent applications received in recent years is given by the equation below, where $ t $ represents the number of years since 2000 and $ p $ represents the number of design patents (in thousands). In 2017, the number of applications for a design patent was 43,340.\[ p'(t) = 0.0102t + 2.03 \]Complete parts (a) and (b) below.---(a) Find the function that gives the total number (in thousands) of design patent applications received in year $ t $.\[ p(t) = \]*(Type an exact answer.)*

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Answered: The approximate rate of change in the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

An electric company uses time-of-day pricing to encourage cus- tomers to use electricity during times of less demand. From 6 P.M. to midnight, the cost is modeled by E(t)= 600/(1+t^2) cents per kilowatt hour, where 6 (< or =) t (< or =) 12 is measured in hours after noon. How much does it cost to use one kilowatt of electricity over this 6-hour period?
A tank holds 200 gal of water that contains 40 lb of dissolved salt. A brine (salt) solution is flowing into the tank at the rate of 2 gal per minute while the solution flows out at the same rate. The brine solution entering the tank has a salt concentration of 4 lb per gal. (a) Find a function that represents the amount of salt in the tank at any time. (b) As time passes, what happens to the salt concentration?
a retail store estimates that weekly sales s and weekly advertising costs x both in dollars are related by s=40,000-30000e^-0.00025x. The current weekly advertising cost are $4,000 and these costs are increasing at a rate of $400 per week. Find the current rate of change of sales
6) From 2004 through 2013, the sales per share S (in dollars) for Dollar Tree can be modeled by S= (0.0120t² + 0.140t + 2.30)", 4
The function v(x) = 20,000(0.87)* models the value of a car x years afterits purchase. Which best describes the rate of change in the value of thecar?
The revenue (in thousands of dollars) from producing x units of an item is modeled by R(x)=8x-0.01x^2. Find the average rate of change in revenue as x changes from 1004 to 1006.
The population of the town of Missed Chances has, since January 1, 1973, been described by the function P=45000(1.04)^t where PP is the population tt years after the start of 1973. At what rate was the population changing on January 1, 1998?
Consider the function that assigns to each number x the value 3x^2 (three x to the second power). a. Find the output assigned to each input listed in the table. Input (x) Output (3x^2) -2 -1 0 1 b. The average rate of change of the function using the rows for x = -2 and x = -1 from the table is ____________. c. The average rate of change of the function using rows for x = 0 and x = 1 from the table is ____________. d. Do you think the function is linear or nonlinear? Answer choices; 1. Linear 2. Nonlinear Explain your answer.

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