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# Constructing exponential models

Sal models the distribution of a chain letter using an exponential function.

## Want to join the conversation?

• cant we just write a function for the rate of change per week instead of every three weeks? I find it easier to write a function in case t is not a multiple of 3, i.e. f(t)=40*1.3^t. Since it grows 90% every three weeks, it would grow 30% every week, i.e. 1.3.
• you will have to change your rate
(1 vote)
• How do I find what "A" is if I try to convert 40*1.9^(t/3) to 40*A^t.
My goal is to find "A" and know the weekly rate of email chain growth.
• You have 40 * 1.9^(t/3) and want it in the form 40 * A^t.
Note that 1.9^(t/3) = [ 1.9^(1/3) ]^t
and then use the calculator to find the value of 1.9^(1/3) which equals A.
Then interpret the value of A to give you the weekly rate of e-mail chain growth.
OK?
• Shouldn't the answer be 40.((1.9)^[t/3]) rather than 40.((1.9)^(t/3))? (greatest integer function)
• With (t/3) you can get an answer for any week, while [t/3] rounds up to answers for multiples of 3 weeks.
• What would you do with decay functions? Would you still add the +1 like he did for the 9/10?
• The 1 represents that you start with 100%. For a decay problem, the 100% decreases, so we subtract.
So, you would use: 1 - decay percentage.
Hope this helps.
• Why is it P(t) and not simply just P in the exponential function and table?
(1 vote)
• The problems asks you to "write a function". Functions are written using function notation, which is why Sal uses P(t) rather than just P.
• Are you guys 10th graders?
• How come at he is multiplying by 1.9. Aren't you supposed to multiply it by 0.9 or 90% ?
• 10 * 1.9 = 19 - 90% increase
10 * 0.9 = 9 - 10% reduction
• Derek has more friends than most people at my school.
• At , why is it that 40+9/10*40 equal to 40(1+9/10)?
(1 vote)
• I don't understand how he goes from 40 * (9/10) + 40 to 40(1 + (9/10)) ? Like, I thought it was factoring but how do you factor a 40 out of 9/10 ?

Here's what I tried:

(40)(40 + (9/10)) // factor out a 40 from each set of parens
(40)(1)(1 + ?) // if 9/10 was divisible by 40, here's where you'd put (9/10) / 40, but it's not so I dunno what I'm missing

40(1 + (9/10)) // this is what Sal ends up with

Btw, I did the math and confirmed that 40 * (9/10) + 40 does equal 40(1 + (9/10)), so my only conclusion is that I'm missing something about how to factor stuff?
(1 vote)
• You changed "40 times 9/10" into "40 plus 9/10". This is why your version isn't working.
40*9/10, you can factor out the 40 and end up with 9/10.

Hope this helps.