Another look at the number e

​This Quizizz is an activity about the number e

On the next slide is a video with a little more background info. Then there will be some question slides. Enjoy!

Fill in the Blanks

To see how the irrational value of e develops by increasing the value of n in the limit definition of e , let's evaluate a few examples as the value of n gets bigger

Evaluate $\left(1+\frac{1}{5}\right)^5$ =

Round your answer to the 3rd decimal place.

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Let the value of n get bigger: Evaluate $\left(1+\frac{1}{n}\right)^n$ for n = 10.

Round your answer to 3 decimal places

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Let the value of n get bigger: Evaluate $\left(1+\frac{1}{n}\right)^n$ for n = 50.

Round your answer to 3 decimal places

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Let the value of n get bigger: Evaluate $\left(1+\frac{1}{n}\right)^n$ for n = 100.

Round your answer to 3 decimal places

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Let the value of n get bigger: Evaluate $\left(1+\frac{1}{n}\right)^n$ for n = 500.

Round your answer to 3 decimal places

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Let the value of n get bigger: Evaluate $\left(1+\frac{1}{n}\right)^n$ for n = 800.

Round your answer to 3 decimal places

Multiple Choice

What do we notice about the values of the expression $$\left(1+\frac{1}{n}\right)^n$$ as n gets bigger and bigger?

• They get closer and closer to the decimal value of 2.71828...

• They get closer and closer to 0

• They get closer and closer to $$\infty$$

Multiple Choice

Who first gave the number 2.718281828459... the name e

• Leonhard Euler

• Daniel Bernoulli

• Carl Gauss

• Gottfried Leibniz

Multiple Choice

What type of math problem was Leonhard Euler attempting to solve when he calculated out the many decimal places for e?

• How much interest is earned from a sum of money if the amount compounds continuously

• How to calculate the rate at which rain drops fall

• How to calculate the area of a circle

• How to create a never ending fraction formula

Match

Match the following:

• $$\ln\left(e\right)$$

• $$e^3$$

• $$\ln\left(e^3\right)$$

• $$e^1$$

• $$e^{\ln\left(5\right)}$$

1

~ 20.086

3

~ 2.718

5

• 1

• ~ 20.086

• 3

• ~ 2.718

• 5

Fill in the Blanks

Solve the following equation. Leave your answer in "exact form". (Exact form means to leave in terms of ln)

$5\cdot e^{\left(x+1\right)}-4=11$

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If $\ln\left(x\right)\ =\ 7$ , what does x equal?

(Leave your answer in terms of e. You can use the "^" symbol to represent an exponent.)

Multiple Choice

TRUE or FALSE: $$\ln\left(x\right)\ =\ e^x$$

• True

• False

Multiple Choice

TRUE or FALSE: If $$y=\ln\left(x\right)$$ then $$x=e^y$$

• True

• False

Multiple Select

Which of the following are true statements? Select all that apply:

• ln(1) = 0

• $$e^2\sim7.389$$

• $$\ln\left(e\right)=2.71828...$$

• $$\ln\left(1\right)=e$$

• $$\ln\left(e^8\right)=8$$