The initial size of a population is 1000, and it has the given instantaneous growth or decay rate per year. -85% (a) Find an exponential model f(x) = Ce"* for the population, where x is measured in years. f(x) = ||

The initial size of a population is 1000, and it has the given instantaneous growth or decay rate per year. -85% (a) Find an exponential model f(x) = Ce"* for the population, where x is measured in years. f(x) = ||

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 61SE: The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012,...

See similar textbooks

Related questions

Q: The half-life of a certain substance is 17 years. How long will it take for a sample of this…

A: The half‐life of a certain substance is 17 years. To determine how long it will take for a sample of…

Q: The half-life of caffeine in a healthy adult's bloodstream is 5.7 hours. Suppose Alex, a healthy…

A: For a exponential equation of the form, A=A'ekt, A' is initial value and k is growth rate.

Q: The half-life of cobalt 60 is 5 years. (a) Obtain an exponential decay model for cobalt 60 in the…

A: (a) It is given that the half life of cobalt 60 is 5 years. The exponential decay model for cobalt…

Q: Radium disintegrates at a rate proportional to instantaneously present. If the half - life of…

A: Let the amount of Radium after t years be given by R(t). The rate of disintegration is dRdt.…

Q: A population numbers 19.000 organisms Initially and decreases by 5,2% each year. Suppose Prepresents…

A: Given that Population= 19000 organisms Decreased rate= 5.2%each year.

Q: A bacterial population is known to have a logistic growth pattern with initial population 1000 and…

A: As per Bartleby guidelines, we are allowed to answer one question per query. Given : Initial…

Q: A population numbers 10,000 organisms initially and grows by 2.6% each year. Suppose P represents…

A: Given data : Population numbers = 10,000 Population , P = abt

Q: 41. Time Required to Reach a Goal How many years will it take for an initial investment of $10,000…

A: Consider that the initial investment of $10,000 compounded annually to grow to $25000, with rate of…

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A: Given:

Q: The half-life of caffeine in a healthy adult's bloodstream is 5.7 hours. Suppose Alex, a healthy…

Q: Let P = P(t) be a quantity that obeys an exponential growth law with growth constant k. Show that P…

Q: The population of a town is 2,500 people, and is decreasing at a rate of 3.5% per year. Write an…

A: Exponential Decay function Y = a(1-r)^t

Q: The population of a town with a 2016 population of 63,000 grows at a rate of 2.4% per year. a.…

Q: The population of a town with a 2016 population of 105,000 grows at a rate of 1.9% per year. a. Find…

Q: A population numbers 12,000 organisms initially and grows by 13.4% each year. Suppose P represents…

A: Consider the given information: Initial population is 12000. Growth rate is 13.4% each. Hence,…

Q: 10. A population is declining at a continuous rate of 3% per day. If there were 20 in the population…

A: Question- 10. A population is declining at a continuous rate of 3% per day. If there were 20 in the…

Q: A population grows according to an exponential growth model. The initial population is Po=4, and the…

Q: The initial size of a population is 1000, and it has the given instantaneous growth or decay rate…

A: Given: The initial size of a population is 1000, and it has the given instantaneous growth or decay…

Q: A recently installed machine earns the company revenue at a continuous rate of 60,000t + 45,000…

A: (a) We have to find the present value of the revenue earned by the machine during the first year of…

Q: a function decreases by 5% each year, then the yearly decay factor is?

A: Subtract rate from 1 for decay factor

Q: 1094 26. A pizza is removed from the oven at a temperature of 425 F. After 15 minutes, the pizza has…

A: 26. initial temperature a = 425 F time t = 15 minutes final temperature y= 200 F exponential…

Q: A population P is initially 850. Find an exponential growth model in terms of the number of time…

A: Given Initial population = 850 decreased rate = 9% number of time periods =x

Q: Time Required to Reach a Goal How many years will ittake for an initial investment of $25,000 to…

A: The interest formula for compounded continuously is: A=Pert Where, A is the future amount or…

Q: Following the birth of a child, a parent wants to make an initial investment P0 that will grow to…

A: Given: Initial investment p0 that will grow to 60,000 for the child education at age 17 interest is…

Q: 9. Find an exponential function of the form Y = ab" whose graph passes through the points -3, and…

A: NOTE: Refresh your page if you can't see any equations. . the exponential function is in the form of…

Q: Bacterial growth is the proliferation of bacterium into two daughter cells, in a process called…

Q: A population numbers 19,000 organisms initially and decreases by 5.4% each year. Suppose PP…

A: Given data: The initial population is 19,000. The decrease in growth is r=5.4%=0.054.

Q: 3) An endangered species of fish has a population that is decreasing exponentially (A = Agekt). The…

A: The endangered species of fish has a population that decreasing exponentially as…

Q: tion 13 The population of a town with an initial population of 68,555 grows at a rate of 3.8% per…

Q: 16. The world population in 1975 was approximately 4 billion, and was determined to be growing…

A: Given: The population growth function is ft=4e0.019t, where t is the number of years. To find: The…

Q: A population P is initially 550. Find an exponential growth model in terms of the number of time…

A: Given Data: The initial population is: Pi=550 The population in each time period is: Pr=3Pi The…

Q: Sales of a textbook have been declining continuously at a rate of 5% per year since the year 2015…

A: Given: A(t)=Aert

Q: A population numbers 12,000 organisms initially and grows by 9.9% each year. Suppose P represents…

A: Given, Population number= 12000 Grows by 9.9%=9.9100=0.099

Q: A population numbers 16,000 organisms initially and grows by 10.2% each year. Suppose P represents…

Q: The population of Ukraine in 2015 was 44.4 million and the expected continuous annual rate of change…

A: The exponential growth model is given by the formula where A is initial population, k is the annual…

Q: The number of bacteria in a culture decreases according to a continuous exponential decay model. The…

A: Exponential decay is given by :y=y0e-ktwhere y0=initial populationk = decay constantt = time

Q: A certain population has a yearly per capita growth of 2.2%, and the initial value is 2 million. Use…

Q: 1. You invest $200 at 10% annual interest compounded continuously. How much do you have after 5…

Q: A population numbers 20,000 organisms initially and grows by 15.1% each year. Suppose P represents…

Q: 12. Under ideal conditions, a population of rabbits has an exponential growth rate of 11.7% per day.…

A: Here we will find the time in days to have 500,

Q: The number of bacteria in a certain population is predicted to increase according to a continuous…

A: Given problem The number of bacteria in a certain population is predicted to increase according to a…

Q: Using the concept of exponential growth and exponential decay. Solve the given problem. 1. A small…

A: Exponential equation of the form Where P(x) represents the population after x years and ‘a’…

Q: 1. Suppose that the number of bacteria in a certain population increases according to a continuous…

Q: A population P is initially 350. Find an exponential growth model in terms of the number of time…

A: Let P = population after x periods P0 = initial population =350 t= time P=P0ert P increases by 100%…

Q: 6. Find dthe time required for an investment of $10,000 to grow to $18,000 at an annual interest…

A: 6) Given: P=$10,000, A=$18,000 and r=6%=0.06. The Compound Interest Formula is given by, A=P1+rnnt…

Q: The exponential function f(x) = A · Bº crosses the y-axis at the point (0, 2100) and has a decay…

Q: 17) Consider the exponential function f(x) = 9e0.043t. %3D Is the function growing or decaying? What…

A: Topic:- function

Q: Find the associated exponential decay of growth model. Q = 1,700 when t = 0; half-life = 1.

A: The exponential decay of the growth model is Qt=Q0e-kt where k=ln 2Half life. Here, Half life=1…

Q: The mass of a substance, which follows a continuous exponential growth model, is being studied in a…

A: Answer

Q: A population numbers 12,000 organisms initially and decreases by 1.8% each year. Suppose Prepresents…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The initial size of a population is 1000, and it has the given instantaneous growth or decay rate per year.
-85%
(a) Find an exponential model f(x) = Cex for the population, where x is measured in years.
f(x) = ||

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

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.

Similar questions

An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?
An investment account with an annual interest rateof 7 was opened with an initial deposit of 4,000 Compare the values of the account after 9 yearswhen the interest is compounded annually, quarterly,monthly, and continuously.
What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?
The table shows the mid-year populations (in millions) of five countries in 2015 and the projected populations (in millions) for the year 2025. (a) Find the exponential growth or decay model y=aebt or y=aebt for the population of each country by letting t=15 correspond to 2015. Use the model to predict the population of each country in 2035. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation y=aebt gives the growth rate? Discuss the relationship between the different growth rates and the magnitude of the constant.
The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012, therewere 23,900 fox counted in the area. What is the foxpopulation predicted to be in the year 2020 ?