Suppose that the sales at Borders bookstores went from 62 million dollars in 1992 to 427 million dollars in 1994. Find an exponential function to model the sales (in millions of dollars) as a function of years (t) since 1992.
sales=_______ millions of dollars
What is the continuous percent growth rate, per year, of sales?
continuous growth rate =

Question

Suppose that the sales at Borders bookstores went from 62 million dollars in 1992 to 427 million dollars in 1994. Find an exponential function to model the sales (in millions of dollars) as a function of years (t) since 1992.
sales=_______ millions of dollars
What is the continuous percent growth rate, per year, of sales? 
continuous growth rate =

anonymous · Answer

Have you started it or tried anything yet?

anonymous · Answer

I dont even know where to begin

anonymous · Answer

start time at 1992   ie t=0 there...

anonymous · Answer

so t=2 in 1994

anonymous · Answer

ok that makes sense

anonymous · Answer

your expression  the looks like   427= 62*e^(c*2)

anonymous · Answer

so how do i find e and c relative to sales in millions of dollars

anonymous · Answer

and the general expression is   62*e^(c*t)    (you'll need to use the first expression I gave to find 'c'

anonymous · Answer

hmm so should i put t as 0?

anonymous · Answer

t=0 in 1992

anonymous · Answer

i mean to find c

anonymous · Answer

427= 62*e^(c*2)

use natural log to find c

anonymous · Answer

(and algebra)

anonymous · Answer

ok sorry my prof touched very lightly on this stuff. So can you tell me what i take the logs of is it log of both sides?

anonymous · Answer

yep

anonymous · Answer

simplify a bit first to make your life easier...

anonymous · Answer

so is it log of 427 and log of 62? or is itlog62e^elog2

anonymous · Answer

$$\ln (e ^{value}) = value$$

anonymous · Answer

ie natural log 'undoes' e^

anonymous · Answer

divide both sides by 427 first, then take the natural log of both sides

anonymous · Answer

so is it 427/427= (ln62*e^(c*2))/427

anonymous · Answer

wait you said the log gets rid of the e^

anonymous · Answer

yes... actually   I should have said divide both sides by 62    got it turned around...   do that and then take the natural log of both sides...

anonymous · Answer

so then (427/62)=6.8870=....

anonymous · Answer

=ln2/62?

anonymous · Answer

....
try using the draw feature to show me what you're doing and I can check it

anonymous · Answer

ok u said divide both sides by 62 and the first equation you told me to set up was 427= 62*e^(c*2). So i did (427/62)=((ln2)/62) because you said the natural log gets rid of the e^ and you said divide both sides by 62.

anonymous · Answer

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