Annette Arroyo
2021-03-06
Answered

Create an example of sequence of numbers with an exponential growth pattern, and explain how you know that the growth is exponential.

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komunidadO

Answered 2021-03-07
Author has **86** answers

In the exponential patterns, the successive numbers increase or decreases by the same percent.

Exponential growth patterns: A sequence of numbers has an exponential pattern when each successive number increase by the same percentage.

There is one simple example of a sequence of an exponential growth:

The population of a dogs doubled every year and the sequence is given as:

2, 4, 8, 16, 32, 64, 128, 256 etc.

In the exponential function, over the time t values of function increase very fast.

Now, the formula for exponential growth function is:

asked 2021-02-12

At the beginning of an environmental study, ad forest covered an area of $1500k{m}^{2}$ .Since then, this area has decreased by 3.75% each year.Let t be the number of years since the start of the study.Let y be the area that the forest covers in $k{m}^{2}$ .

Write an exponential function showing relationship between y and t.

Write an exponential function showing relationship between y and t.

asked 2021-09-11

A fruit fly population of 24 flies is in a closed container. The number of flies grows exponentially, reaching 384 in 18 days. Find the doubling time (time for the population to double) and write an equation that models this scenario.

asked 2022-03-08

The population of a town increased by 2.54% per year from the beginning of 2000 to the beginning of 2010. The town's population at the beginning of 2000 was 74,860.

asked 2022-02-01

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 number of bactenia ater 15 minutes? (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 number of bactenia ater 15 minutes? (round to the nearest whole number of bacteria.)

asked 2020-10-18

If f(x) is an exponential function where f(−1)=8 and
f(8.5)=87, then find the value of f(3), to the nearest hundredth.

asked 2021-08-19

The function $A=7.7{\left(0.92\right)}^{t}$ represents an exponential growth or decay function.

A.

Does the function P represent exponential growth or decay? B. What is the initial quantity? C. What is the growth or decay factor?

a.

Exponential Growth. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

b.

Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay facotor is 1.08

c.

Exponential Growth. B. The initial quantity is 0.92. C. The growth or decay factor is 1.08

d.

. Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

e.

None of these

A.

Does the function P represent exponential growth or decay? B. What is the initial quantity? C. What is the growth or decay factor?

a.

Exponential Growth. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

b.

Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay facotor is 1.08

c.

Exponential Growth. B. The initial quantity is 0.92. C. The growth or decay factor is 1.08

d.

. Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92

e.

None of these

asked 2022-01-21

Define thew term Exponential Growth and Decay?