The number e (and the exponentiation function ${e}^{x}$) appears in so many places in mathematics and engineering. There seem to be a multitude of applications of it. I want to know why.

frobirrimupyx
2022-09-14
Answered

Why is e so special?

The number e (and the exponentiation function ${e}^{x}$) appears in so many places in mathematics and engineering. There seem to be a multitude of applications of it. I want to know why.

The number e (and the exponentiation function ${e}^{x}$) appears in so many places in mathematics and engineering. There seem to be a multitude of applications of it. I want to know why.

You can still ask an expert for help

asked 2022-03-23

__At the beginning of the year, there are 7650 individuals in a population of beavers whose per capita rate of for the year is 0.18. What is its population growth rate at the end of the year?__

asked 2022-09-18

A Bacteria Culture Contains 100 Cells and Grows at a Rate Proportional to its Size

A bacteria culture contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420.

a) Find and expression for the number of bacteria after t hours

$P(t)=P(0){e}^{kt}=100$

b) Find the number of bacteria after 3 hours.

$P(t)=P(3){e}^{k3}=$ (confused as to how to set this up)

d) When will the population reach 10,000?

A bacteria culture contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420.

a) Find and expression for the number of bacteria after t hours

$P(t)=P(0){e}^{kt}=100$

b) Find the number of bacteria after 3 hours.

$P(t)=P(3){e}^{k3}=$ (confused as to how to set this up)

d) When will the population reach 10,000?

asked 2022-02-01

Give an example of an exponential function in the form $y=a\times {b}^{x}$ that is neither an exponential growth function nor an exponential decay function. Explain your reasoning.

asked 2022-09-12

A Bacteria Culture Grows with Constant Relative Growth Rate.

A micro organism culture Grows with consistent Relative boom rate. The micro organism count number become 400 after 2 hours and 25,six hundred after 6 hours.

a) What is the relative growth rate? Express your answer as a percentage.

Using this formula $P(t)={P}_{0}{e}^{kt}$

$t=time$

$k=growth\text{}rate$

${p}_{0}=initial\text{}amount$

How do I calculate a formula with the information I have?

b) What was the initial size of the culture?

c) Find an expression for the number of bacteria after t hours

d) Find the number of cells after 4.5 hours

e) Find the rate of growth after 4.5 hours

f) When the population reach 50,000?

that is a self look at query. i've Calculus II subsequent semester and sincerely would like to have a clear method as to a way to solve a hassle inclusive of this.

A micro organism culture Grows with consistent Relative boom rate. The micro organism count number become 400 after 2 hours and 25,six hundred after 6 hours.

a) What is the relative growth rate? Express your answer as a percentage.

Using this formula $P(t)={P}_{0}{e}^{kt}$

$t=time$

$k=growth\text{}rate$

${p}_{0}=initial\text{}amount$

How do I calculate a formula with the information I have?

b) What was the initial size of the culture?

c) Find an expression for the number of bacteria after t hours

d) Find the number of cells after 4.5 hours

e) Find the rate of growth after 4.5 hours

f) When the population reach 50,000?

that is a self look at query. i've Calculus II subsequent semester and sincerely would like to have a clear method as to a way to solve a hassle inclusive of this.

asked 2022-01-19

Consider the model for exponential growth or decay given by $A={A}_{0}{e}^{kt}.$

If k_____ , the function models the amount, or size,of a growing entity. If k_____ , the function models the amount, or size, of a decaying entity.

If k_____ , the function models the amount, or size,of a growing entity. If k_____ , the function models the amount, or size, of a decaying entity.

asked 2021-05-26

Tell whether the function represents exponential growth or exponential decay. Explain your reasoning.

asked 2021-06-26

State whether the equation represents exponential growth, exponential decay, or neither.