Explanation Calculation: The rate of growth of A with respect to t is d A d t = 0.01 A . Use variable separable method and integrate the differential equation. d A A = 0.01 d t ∫ 1 A d A = 0.01 ∫ d t ln | A | = 0.01 t + C Take exponential on both sides, e ln | A | = e ( 0.01 t + C ) A = e 0.01 t e C Ȁ

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 5.3, Problem 78E

To determine

To find: The amount A in an account after t years if the rate of growth of A with respect to t is $dAdt=0.01A$ and $A(0)=5,250$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.3, Problem 77E

Chapter 5.3, Problem 79E

Students have asked these similar questions

For the distribution shown, match the letter to the measure of central tendency. A B C C Drag each of the letters into the appropriate measure of central tendency. Mean C Median A Mode B

A physician who has a group of 38 female patients aged 18 to 24 on a special diet wishes to estimate the effect of the diet on total serum cholesterol. For this group, their average serum cholesterol is 188.4 (measured in mg/100mL). Suppose that the total serum cholesterol measurements are normally distributed with standard deviation of 40.7. (a) Find a 95% confidence interval of the mean serum cholesterol of patients on the special diet.

The accompanying data represent the weights (in grams) of a simple random sample of 10 M&M plain candies. Determine the shape of the distribution of weights of M&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the weight of a plain M&M? Click the icon to view the candy weight data. Draw a frequency histogram. Choose the correct graph below. ○ A. ○ C. Frequency Weight of Plain M and Ms 0.78 0.84 Frequency OONAG 0.78 B. 0.9 0.96 Weight (grams) Weight of Plain M and Ms 0.84 0.9 0.96 Weight (grams) ○ D. Candy Weights 0.85 0.79 0.85 0.89 0.94 0.86 0.91 0.86 0.87 0.87 - Frequency ☑ Frequency 67200 0.78 → Weight of Plain M and Ms 0.9 0.96 0.84 Weight (grams) Weight of Plain M and Ms 0.78 0.84 Weight (grams) 0.9 0.96 →

Chapter 5 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 5.1 - Matched Problem 1 Note that ddx(x3)=3x2 A. Find...Ch. 5.1 - Find each indefinite integral: (A) 2dx (B) 16etdt...Ch. 5.1 - Matched Problem 3 Find each indefinite integral:...Ch. 5.1 - Matched Problem 4 Find the equation of the curve...Ch. 5.1 - Matched Problem 5 Find the revenue function R(x)...Ch. 5.1 - Matched Problem 6 There are currently 64,000...Ch. 5.1 - Explore and Discuss 1 Formulas 1, 2, and 3 do not...Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - In Problems 18, write each function as a sum of...Ch. 5.1 - In Problems 18, write each function as a sum of...

Knowledge Booster

Learn more about

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

The amount A in an account after t years if the rate of growth of A with respect to t is d A d t = 0.01 A and A ( 0 ) = 5 , 250 .

Solution Summary: The author calculates the rate of growth of A with respect to t by using a variable separable method and integrating the differential equation.

Concept explainers

Videos

To find: The amount A in an account after t years if the rate of growth of A with respect to t is $dAdt=0.01A$ and $A(0)=5,250$ .

Want to see the full answer?

Chapter 5 Solutions