Recent questions in Exponential growth and decay

Algebra IAnswered question

spiderifilms6e 2022-01-31

An unknown radioactive element decays into non-radioactive substances. In 720 days the radioactivity of a sample decreases by 33 percent.

(a) What is the half-life of the element? half-life:_____

(6) How long will it take for a sample of 100 mg to decay to 47 mg? time needed:____

(a) What is the half-life of the element? half-life:_____

(6) How long will it take for a sample of 100 mg to decay to 47 mg? time needed:____

Algebra IAnswered question

Adrian Cervantes 2022-01-31

Describe what the values of C and k represent in the exponential growth and decay model $y=C{e}^{kt}$ .

Algebra IAnswered question

Jacquelyn Sanders 2022-01-30

Rewrite the function to determine whether it represents exponential growth or exponential decay.

$y=2{\left(1.06\right)}^{9t}$

Algebra IAnswered question

Alvin Pugh 2022-01-30

The half-life of a radioactive kind of xenon is 9 hours. If you start with 32 grams of it, how
much will be left after 18 hours?

Algebra IAnswered question

Kaydence Huff 2022-01-30

Solve problems involving antiditerentiation

Solve situational problems involving exponential growth and decay

1. The rate of decay of radium is said to be proportional to the amount of radium present. If the half-life of radium is 1690 years and there are 200 grams on hand now, how much radium will be present in 845 years?

Solve situational problems involving exponential growth and decay

1. The rate of decay of radium is said to be proportional to the amount of radium present. If the half-life of radium is 1690 years and there are 200 grams on hand now, how much radium will be present in 845 years?

Algebra IAnswered question

Hailee Cline 2022-01-30

Using the concept of exponential growth and exponential decay, solve the given problem. Show complete and systematic solutions.

1. An unknown radioactive element decreases 12% of its amount every 5 days. What is exponential function? that describes the amount left after t days? If there are 300g of the substance at present, how much is left after 30 days? (round off the value up to two decimal places)

1. An unknown radioactive element decreases 12% of its amount every 5 days. What is exponential function? that describes the amount left after t days? If there are 300g of the substance at present, how much is left after 30 days? (round off the value up to two decimal places)

Algebra IAnswered question

Jenny Branch 2022-01-30

A car's value decreases at a rate of 5% annually. The car was worth $32,000 in 2010. Find the car's 2013 market value.

Step 1: Decide whether it is growing or decaying

Step 2: Solve for the rate:

Step 3: solve

Algebra IAnswered question

Jamya Elliott 2022-01-30

Tell whether the function represents exponential growth or exponential decay. Then graph the function.

$y={\left(1.8\right)}^{x}$

Algebra IAnswered question

meteraiqn 2022-01-30

Solve the following problems involving exponential growth and decay.

The half-life of carbon-14 1s approximately 6000 years. How much of 800 g of this substance will remain after 30,000 years?

The half-life of carbon-14 1s approximately 6000 years. How much of 800 g of this substance will remain after 30,000 years?

Algebra IAnswered question

Turnseeuw 2022-01-30

Exponential Growth and Decay

Exponential growth and decay problems follow the model given by the equation$A\left(t\right)=P{e}^{rt}$

-The model is a function of time t

-A(t) is the amount we have ater time t

-PIs the initial amount, because for t=0, notice how$A\left(0\right)=P{e}^{0\times t}=P{e}^{0}=P$

-Tis the growth or decay rate. It is positive for growth and negative for decay

Growth and decay problems can deal with money (interest compounded continuously), bacteria growth, radioactive decay. population growth etc.

So A(t) can represent any of these depending on the problem.

Practice

The growth of a certain bactenia population can be modeled by the function

$A\left(t\right)=900{e}^{0.0534}$

where A(t) is the number of bacteria and t represents the time in minutes.

How long will t take for the number of bacteria to double? (your answer must be accurate to at least 3 decimal places.)

Exponential growth and decay problems follow the model given by the equation

-The model is a function of time t

-A(t) is the amount we have ater time t

-PIs the initial amount, because for t=0, notice how

-Tis the growth or decay rate. It is positive for growth and negative for decay

Growth and decay problems can deal with money (interest compounded continuously), bacteria growth, radioactive decay. population growth etc.

So A(t) can represent any of these depending on the problem.

Practice

The growth of a certain bactenia population can be modeled by the function

where A(t) is the number of bacteria and t represents the time in minutes.

How long will t take for the number of bacteria to double? (your answer must be accurate to at least 3 decimal places.)

Algebra IAnswered question

trefoniu1 2022-01-29

Does a group with exponential growth always have a hyperbolic subgroup which has exponential growth?

Algebra IAnswered question

logosomatw 2022-01-29

Look at the group of microorganisms that was mentioned earlier. According to the function f(t) = 200e02, where t is measured in minutes, this population expands. A. After five hours (or 300 minutes), how many germs are still in the population? B. When does the number of bacteria reach 100,000?

Algebra IAnswered question

amevaa0y 2022-01-29

Explain when a function in the form

$y=a\times {b}^{x}$

models exponential growth and when it models exponential decay.

models exponential growth and when it models exponential decay.

Algebra IAnswered question

Selena Cowan 2022-01-29

A certain radioactive substance has a half-life of 12 days. This means that every 12 days, half of the
original amount of the substance decays. If there are 128 milligrams of the radioactive substance
today, how many milligrams will be left after 48 days?

Algebra IAnswered question

Carly Shannon 2022-01-29

Exponential Growth and Decay

Exponential growth and decay problems follow the model given by the equation$A\left(t\right)=P{e}^{rt}$

-The model is a function of time t

-A(t) is the amount we have ater time t

-PIs the initial amount, because for t=0, notice how$A\left(0\right)=P{e}^{0\times t}=P{e}^{0}=P$

-Tis the growth or decay rate. It is positive for growth and negative for decay

Growth and decay problems can deal with money (interest compounded continuously), bacteria growth, radioactive decay. population growth etc.

So A(t) can represent any of these depending on the problem.

Practice

The growth of a certain bactenia population can be modeled by the function

$A\left(t\right)=900{e}^{0.0534}$

where A(t) is the number of bacteria and t represents the time in minutes.

What is the initial number of bacteria? (round to the nearest whole number of bacteria.)

Exponential growth and decay problems follow the model given by the equation

-The model is a function of time t

-A(t) is the amount we have ater time t

-PIs the initial amount, because for t=0, notice how

-Tis the growth or decay rate. It is positive for growth and negative for decay

Growth and decay problems can deal with money (interest compounded continuously), bacteria growth, radioactive decay. population growth etc.

So A(t) can represent any of these depending on the problem.

Practice

The growth of a certain bactenia population can be modeled by the function

where A(t) is the number of bacteria and t represents the time in minutes.

What is the initial number of bacteria? (round to the nearest whole number of bacteria.)

Algebra IAnswered question

Celia Horne 2022-01-29

Exponential Growth /Decay
Model

Given exponential growth or decay the amoun tP after time tis given by the following formula:

$P={P}_{0}{e}^{kt}$

Here$P}_{0$ is the initial amount and k is the exponential growth/decay rate.

Now you are ready to complete the following:

a) As stated previously the statement - The rate of change of variable y is proportional to the value of y-describes a differential equation. Write this differential equation.

Given exponential growth or decay the amoun tP after time tis given by the following formula:

Here

Now you are ready to complete the following:

a) As stated previously the statement - The rate of change of variable y is proportional to the value of y-describes a differential equation. Write this differential equation.

Algebra IAnswered question

Carla Murphy 2022-01-22

Communicate Precisely How are exponential growth functions similar to exponential decay functions? How are they different?

Algebra IAnswered question

Roger Smith 2022-01-22

In the exponential growth or decay function, explain the circumstances that cause k to be positive or negative.

Algebra IAnswered question

Kathy Williams 2022-01-22

Prove that if $y={y}^{0ekt},$ where $y}_{0$ and k are constants, then
$\frac{dy}{dt}=ky$

(This says that for exponential growth and decay, the rate of change of the population is proportional to the size of the population, and the constant of proportionality is the growth or decay constant.)

(This says that for exponential growth and decay, the rate of change of the population is proportional to the size of the population, and the constant of proportionality is the growth or decay constant.)

Exponential growth and decay subject related to one of the more complex aspects of Algebra, which makes it relatively difficult for students to cope with it as it requires analysis and knowledge of the basics. Take your time to explore various exponential growth and decay practice answers below to refresh your memory and see some helpful examples.

The answers that you can see below must be linked to the questions to see the reasons why certain solutions have been provided. Remember that analysis will be helpful to see the correct approach!