# Talk:Exponential Growth

Chris 10:26, 27 June 2012 (EDT): Chengying, this page is definitely accessible for high school students, and it moves nicely from Algebra 1 through Algebra 2 and ventures into Calculus. I like your ideas for integrating animations into this so that the reader can more easily grasp the limit concept.

The focus in my editing is on clarity of writing.

# Basic Description

Chris 10:26, 27 June 2012 (EDT):
Your first sentence could describe any number of functions. What distinguishes an exponential function from other functions?

Since you are describing both growth and decay and your first example 2^x involves growth, it might make sense to have your second example focus on decay.

Table: Consider organizing the six values in ascending or descending order numerically.

Sentence after table: Isn't what determines an exponential function the presence of a variable in the exponent? Are you talking about situations in which the formula isn't given?
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# General Formula

## For the Discrete Case

Chris 10:26, 27 June 2012 (EDT):

• For the Discrete Case: clearly written; I have one minor suggestion:

Switch "interest compounding problem" to "compounded interest problem "

• Exponential Growth: Compound Interest

Sentence #2 (S2): Change "Assume that you are not going to withdraw this \$1000 in the middle of any year and the interest rate is kept constant. How much money will you end up with after 1 years?" to "Assuming no other deposits or withdrawals and a constant interest rate, what will be the value of the account after t years?"

The "Each year..." is the beginning of your answer, but it appears to be located in the same paragraph as the problem. I don't think it's necessary.

• Exponential Decay: Elimination of Drug from the Body

S2: Change "Suppose the initial amount of a drug is in the body 200mg" to "Suppose the initial amount of a drug in the body is 200mg"
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Swu2 11:12, 6 July 2012 (EDT)"x" to "t"; Also maybe you wanna say "function value" instead of "function size" in the middle paragraph? --CHECK

## For the Continuous Case

Chris 10:26, 27 June 2012 (EDT):
Change "interest rage compounding problem" to "compounded interest rate problem".

I believe the formula for x(t) should have n*t, not t/n in the exponent. Since n is the number of times the bank compounds interest annually, it gets multiplied by t, not divided into it.

Table: I would go to at least two decimal points since money is calculated in dollars and cents. I would also consider changing the numbers in the "number of times interest is compounded per year" column so that there are much larger numbers than 10 in the column next to e.

e mouseover: Change "approximately equals to 2.71828" to "approximately equals 2.71828."

A strange thing happens when you use the online calculator. We should talk about it directly.
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# Half-Life Decay

Chris 10:26, 27 June 2012 (EDT):
After deriving the formula for half-life time t, would it make sense to write the numerical value for ln(1/2) to the nearest three or so decimal places?
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# Doubling Time and the Rule of 70

Chris 10:26, 27 June 2012 (EDT):
To "If the percentage rate is x%, the percentage number is just x", add "not .01x."

Math Behind section: Instead of "alternatively," say "We can then multiply..."
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# Exponential vs. Polynomial Growth

Chris 10:26, 27 June 2012 (EDT):
Do you want to refer to calculus here to support your statements about rate of change?
-- I added a short paragraph about calculus. Anything else I should expand to??
King's Problem link goes to the Bedsheet Problem.
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