(a) Explanation Given: Consider the projected year-end assets function, A ( t ) = 0.0000329 t 3 − 0.00450 t 2 + 0.0613 t + 2.34 where 0 ≤ t ≤ 50 is the number of years since 2000. Definition used: Critical point: A point whose x- coordinate is the critical number c such that either f ′ ( c ) = 0 or f ′ ( c ) does not exists and y -coordinate is f ( c ) . Calculation: Obtain the derivative of the function as follows. A ′ ( t ) = 0.0000329 ( 3 t 2 ) − 0.00450 ( 2 t ) + 0.0613 ( 1 ) + 0 = 0.0000987 t 2 − 0.009 t + 0.0613 Assume c as a critical number such that A ′ ( c ) = 0 or A ′ ( c ) does not exist and obtain its value. 0.0000987 c 2 − 0.009 c + 0.0613 = 0 Use quadratic formula to find the values of c as follows. c = 0.009 ± ( − 0.009 ) 2 − 4 ( 0.0000987 ) ( 0.0613 ) 2 × 0.0000987 Thus, the values of c on computation are 83.77 and 7.414. There is only one critical number c that lies in the range 0 ≤ t ≤ 50 which is c = 7.414 . These points determine the interval ( − ∞ , 0 ) , ( 0 , 7.414 ) , ( 7 (b) To determine To find: The intervals where the function A ( t ) decreases.

10th Edition

ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 13.1, Problem 49E

(a)

To determine

To find: The intervals where the function A(t) increases.

(b)

To determine

To find: The intervals where the function A(t) decreases.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.1, Problem 48E

Chapter 13.1, Problem 50E

Students have asked these similar questions

The price, p, of a specific used car that is x years old is given by the following formula. p(x)=19937(0.86)x (a) How much does a 3-year-old car cost? (b) How much does a 9-year-old car cost? (a) A 3-year-old car costs $_____. (Round to two decimal places as needed.) (b) A 9-year-old car costs$_______. (Round to two decimal places as needed.)

The cost for board exam review services costs P11500, P11750, and P11250 for years 2018, 2019, and 2020 respectively. What is the correct equation to obtain range (in %)? (Range example: From -25% to +15%) a From "[(Average Cost-Lowest Cost)/Average Cost] x 100" to "[(Average Cost-Highest Cost/Average Cost] x 100" O b From "(Lowest Cost/Average Cost) x 100" to "(Highest Cost/Average Cost) x 100" O C. From “[(Lowest Cost-Average Cost)/Average Cost] x 100" to "[[Highest Cost- Average Cost)/Average Cost] x 100" Od. From "(Average Cost/Lowest Cost) x 100" to "(Average Cost/Highest Cost) x 100"

The short-term demand for crude oil in Country A in 2008 can be approximated by -0.06 q=f(p) 2,308,419p where p represents the price of crude oil in dollars per barrel and q represents the per capita consumption of crude oil. Calculate and interpret the elasticity of demand when the price is $85 per barrel. The elasticity of demand for oil is. (Type an integer or a decimal.) What is the elasticity of demand for oil when the the price is $85 per barrel? (Type an integer or a decimal.) Interpret the elasticity of demand. Choose the correct answer below. OA. The demand is elastic, so as price increases, revenue decreases. OB. The demand is elastic, so as price increases, revenue increases. OC. The demand is inelastic, so as price increases, revenue decreases. O D. The demand is inelastic, so as price increases, revenue increases.

Chapter 13 Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

Ch. 13.1 - Find where the function is increasing and...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 1WE Ch. 13.1 - Prob. 2WE Ch. 13.1 - Prob. 3WE Ch. 13.1 - Prob. 4WE Ch. 13.1 - Prob. 5WE Ch. 13.1 - Prob. 6WE

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The intervals where the function A ( t ) increases.

Solution Summary: The author explains that the function A(t) increases in the interval (0,7.414 ).