Answered: Make an exponential model y(t) with the…

Make an exponential model y(t) with the given properties. Assume that t is the number of periods. The initial value is 360, and there is a 9% growth rate per period.

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter10: Exponential And Logarithmic Functions

Section10.5: Solve Exponential And Logarithmic Equations

Problem 10.86TI: Rachel invests $15,000 at age 25. She hopes the investments will be worth when she turns 40. If the...

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: Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt. The count in the…

Q: Use the exponential decay model, A = A, e kt, to solve the following. The half-life of a certain…

A: Solve for the constant by using the following exponential decay: A=A0ektAt t=24,…

Q: In the first six months of the 2014 Ebola outbreak, the total number of reported cases was…

A: There were 100 cases as of April 2014 and it increases continuously at the rate of 72% per month.…

Q: A population numbers 1,650 organisms initially and increases by 6.8% each year. Suppose P represents…

A: The general form of exponential model is, P=P01+rt where, P0 is initial amount, r is rate of growth,…

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: Find an exponential function of the form f(x) = bax + c for the graph.

A: Given function- f(x)= bax+c ----(A) The curve (A) is passing through ( -1,9) So putting x=-1 and…

Q: Use the exponential decay model, A = Ao e k, to solve the following. The half-life of a certain…

A: The half-life of a certain substance is 22 years.

Q: Use the exponential decay model, A=A0ekt, to solve the following. The half-life of a certain…

A: To calculate the decay time of the substance under the given conditons

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: Use the exponential decay model, A = A0ekt, to solve this exercise. The half-life of polonium-210 is…

A: Given half life of polonium-210 is 140 days i.e. in 140 days, the amount becomes half. Using the…

Q: Find a formula for the exponential function passing through the points (-1,-) and (1,8) y% =

Q: Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population…

A: Given : Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal…

Q: In the year 1950, the world population was 2.56 billion people. In 1960, the population grew to 3.04…

Q: Use the exponential decay model, A = A, e kt, to solve the following. The half-life of a certain…

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: Use the exponential decay model, A = Agekt, to solve this exercise. The half-life of polonium-210 is…

A: Consider that exponential decay model of polonium -210 follows: A=A0ekt. Given half life is 140…

Q: A spring is attached to the ceiling and pulled 9 cm down from equilibrium and released. After 2…

Q: Find the half-life of a radioactive element, which decays according to the function A(t)=A0…

Q: The population (in millions) of Canada in 2015 is 35.1 and the expected continuous annual rate of…

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

A: Given: r=85% initial size=1000

Q: The logistic growth function P(x) = models the percentage. P(x), of Americans who are x years old…

A: We have to find the age of American citizens at which 56% of the people has some heart coronary…

Q: Biologists stocked a lake with 600 fish and estimated the carrying capacity to be 3300. The number…

A: Given that the biologists stocked a lake with 600 fish and estimated carrying capacity to be…

Q: Use the exponential decay model, A= Ag e", to solve the following. The half-ife of a certain…

A: Decay model of the substance is given by A=A0ekt. The half-life of certain substance is 22 years.…

Q: Use the exponential decay model, A= A, e", to solve the following. The half-life of a cortain…

Q: Use the exponential decay model, A=A, e, to solve the following. The half-life of a certain…

A: Find the valuer for constant K using the half-life t (1/2) = 19 yrs and then find the decay…

Q: f you invest $10,400 at an interest rate of 2.5% compounded continuously, when will your investment…

Q: The initial size of a bacteria culture that grows exponentially was 10,000. After 1 day, there are…

Q: Use the exponential decay model, A = Ao e kt, to solve the following. The half-life of a certain…

A: Given The half-life period is 21 years, Let the decay model be, A(t) = A0 ekt where k is the decay…

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: determine the time neeessary for P dollars to double when it is invested at interest rate r…

Q: 3 Find a formula for the exponential function passing through the points (-1, ) and (3, 24). y =

Q: Use the exponential decay model, A = A, e kt, to solve the following. The half-life of a certain…

A: A=A00.5tp here half-life is p=21 years here we need to find the time when this substance to decay to…

Q: A spring is attached to the ceiling and pulled 15 cm down from equilibrium and released. After 2…

A: Find the equation for the amplitude in terms of t as variable using the exponential decay equation.

Q: pring is attached to the ceiling and pulled 16 cm down from equilibrium and released. After 4…

Q: After years of overhunting, environmental scientists have reintroduced beavers to Yellowstone…

A: I am going to calculate the required by using the given identity and applying some algebraic…

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: Find an exponential function that has y-intercept 6 and passes through the point (1, 8).

Q: the half life of caffeine in a healthy adult's bloodstream in 5.7 hours. suppose alex, a healthy…

A: Given that, The half life of caffeine in a healthy adult's bloodstream in 5.7 hours. Alex, a healthy…

Q: Suppose Shunreca Garner invested $8000 in stocks and the investment grew exponentially to $10000 in…

A: To use the exponential model to 1) determine the growth rate and 2) to calculate the value after 15…

Q: Use the exponential decay model, A = A, e kt, to solve the following. The half-life of a certain…

Q: A population numbers 16,000 organisms initially and decreases by 2.4% each year. Suppose PP…

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

Q: After a large number of drinks, a person has a blood alcohol level of 200 mg/dL (milligrams per…

Q: Find an exponential function of the form f(x) = bax + c for the graph.

Q: Use the exponential decay model, A = A0ekt, to solve. Round answers to one decimal place. Xanax is a…

A: Given: Xanax is a tranquilizer used in the short-term relief of symptoms of anxiety. Its half-life…

Q: Write the exponential function y=20(1.26)^t in the form y=ae^(kt). a) Once you have rewritten the…

A: Given, The exponential function y=20(1.26)t in the form y=aekt

Q: Write the equation for the exponential function that passes through the points (0, 1) and (3, 53)…

A: The exponential function passes through the points 0,1 and 3,53 with asymptotes as y=-1. Assume the…

Q: Use the exponential decay model, A = Ao e , to solve the following. The half-life of a certain…

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

Make an exponential model y(t) with the given properties. Assume that t is the number of periods.

The initial value is

360,

and there is a

growth rate per period.

y(t) =

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: Model

VIEW

Step 2: Solution

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, algebra and related others by exploring similar questions and additional content below.

Similar questions

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.
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?
Rachel invests $15,000 at age 25. She hopes the investments will be worth when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal?
Hector invests $10,000 at age 21. He hopes the investments will be worth when he turns 50. If the interest compounds continuously, approximately what rate of growth Will he need to achieve his goal?
Jerome invests $18,000 at age 17. He hopes the investments will be worth $30,000 when he turns 26. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Is that a reasonable expectation?
Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.