When records were first kept (t = 0), the population of a rural town was 250 people.

Question:

When records were first kept (t = 0), the population of a rural town was 250 people. During the following years, the population grew at a rate of P'(t) = 30(1 + √t), where t is measured in years.

a. What is the population after 20 years?

b. Find the population P(t) at any time t ≥ 0.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Apr 12, 2019 10:07 AM

The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t = 0), the population was 35...
Consider the following marginal cost functions. a. Find the additional cost incurred in dollars when production is increased from 100 units to 150 units. b. Find the additional cost incurred in...
Consider the following velocity functions. In each case, complete the sentence: The same distance could have been traveled over the given time period at a constant velocity of ________. v(t) = 2 sin...
Suppose the weight of pieces of passenger luggage for domestic airline flights follows a normal distribution with u = 28 pounds and o = 5.7 pounds. (a) Calculate the probability that a piece of...
Suppose that Congress and the president decide that the nation's economic performance is weakening and that the government should "do something" about the situation. They make no tax changes but do...
Make a substitution to express the integrand as a rational function and then evaluate the integral. /1 + x X - dx
Cat Auto Tech. Corp. purchased 10,000 gift certificates from DeJesus. Cat Auto Tech. Corp., an Amoco gasoline station operator, contracted with DeJesus to make 10,000 gift certificates of various...
Bed & Bath, a retailing company, has two departments, Hardware and Linens. The companys most recent monthly contribution format income statement follows: A study indicates that $340,000 of the fixed...
A 15 kg box is given a shove to the right on a horizontal, rough surface. After the hand loses contact, the box's acceleration (using standard directions) is a = (-1.2 m/s, 0). (a) What are the...
The Problem We have currently cash reserves in 10 different currencies in the amounts given in the second column of the following table (in millions). Initial Position Desired Position 70 20 8 3 15 7...
Starting with an initial value of P(0) = 55, the population of a prairie dog community grows at a rate of P'(t) = 20 - t/5 (prairie dogs/month), for 0 t 200, where t is measured in months. a. What...
A culture of bacteria in a Petri dish has an initial population of 1500 cells and grows at a rate (in cells/day) of N'(t) = 100e -0.25t . Assume t is measured in days. a. What is the population after...
Calculate the angular momentum of 7 Li 2 in the J = 5 state.
What should someone be willing to pay for each of the bonds in question 1A.5 if the interest rate doubled to 7 percent? Data from question 1A.5 Determine what someone should be willing to pay for...
You learned that when the minimum efficient scale in a market is smaller, there is likely more competition in the market. How might this observation inform whether higher fixed costs are associated...
For each of the following scenarios, decide whether you agree or disagree and explain your answer. a. Suppose that elasticity of demand for hospital services is -0.15 and that the British government...
What are some primary differences and similarities in governance practices between the United States and other countries?
Steve Collins runs the SC Steak House in London. The restaurant has been in business for 30 years and is one of the most recommended steak houses in London. The total value of the restaurants capital...
The Wendel Stove Company is developing a "professional"- model stove aimed at the home market. The company estimates that variable costs will be $2,700 per unit and fixed costs will be $12,600,000...
Suppose the S&P 500 futures price is 1000, = 30%, r = 5%, = 5%, T = 1, and n = 3. a. What are the prices of European calls and puts for K = $1000? Why do you find the prices to be equal? b. What...
Expand the quotients by partial fractions. 5x 5r 13 (x 3)(x - 2)
The instructions for the integrals have two parts, one for the Trapezoidal Rule and one for Simpsons Rule. I. Using the Trapezoidal Rule a. Estimate the integral with n = 4 steps and find an upper...
Determine which are probability density functions and justify your answer. f(x) = x over [4,8]
Gilbert Canned Produce (GCP) packs and sells three varieties of canned produce: green beans; sweet peas; and tomatoes. The company is currently operating at 82 percent of capacity. Worried about the...
The accounting records of Allen Insulation, Inc. reflected the following balances as of January 1, 20x0: Beginning Inventory: $190 units @ $120 The following transactions occurred in 20x0: January...
Sarasota Limited has a calendar-year accounting period. The following errors were discovered in 2023. 1. The December 31, 2021 merchandise inventory had been understated by $50,400. 2. 3. Merchandise...

When records were first kept (t = 0), the population of a rural town was 250 people.

Question:

Step by Step Answer:

a P20 250 20 3030t dt 250 ...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions