Question

The sales at a particular bookstore grew from $2013 million in 2000 to $3864 million in 2005. Find an exponential function to model the sales as a function of years since 2000. Give your answer using the form B = Bo *a^t.

a.) Bo= millions
b.) a = (exact value)



Please help!! :)

Answer 1

will year 2000 be considered t =0? or t=2000?

Answer 2

I'm not sure I think its 0

Answer 3

ok then if at year 2000, t=0
i will be writing it in the form of a function
B(t) = Bo *a^t -- where Bo and a are constants

we know that B(0)=2013= Bo*a^0
since a^0 = 1, you can quickly solve for Bo

now that you have Bo, solve for a

we know that B(5)=3864=Bo*a^5

so just solve for a

Answer 4

if you're interested in solving it when t=2000 then ill also explain that too you
it is much harder than t=0

Answer 5

you can try that too, just in case.

Answer 6

alright we'll start with the the given function
\[B=B_oa^t\]
find the natural log of both sides
\[ln B=ln ({B_oa^t})\]
using the properties of logs
\[ln B=ln {B_o}+ln ({a^t})\]
still using the properties of logs
\[ln B=ln {B_o}+t*ln ({a})\]

then when you substitute in the actual values, you will get a system of equations
2 equations 2 unknowns.
you just solve that in which ever method you know best

B=2013 when t=2000
B=3864 when t=2005
\[ln (2013)=ln {B_o}+2000*ln (a)\]
\[ln (2864)=ln {B_o}+2005*ln ({a})\]

if it helps, you can substitute
x=ln(B_o)
y=ln(a)
then once you find x and y
B_o=e^x
a=e^y

Answer 7

ln(2013)=x+2000y
ln(2864)=x+2005y

Answer 8

I'm not getting what a is. I got Bo^t is which is 2013 millions.

Answer 9

first method or 2nd method?

Answer 10

first.

Answer 11

Can you just tell me the answer so I can figure it out from there? Please.

Answer 12

3864=2013*a^5

3864/2013=a^5


(3864/2013)^(1/5)=(a^5)^(1/5)

x^(1/5) is the same as the 5th root

a=(3864/2013)^(1/5)

Answer 13

Okay I got it. Thank you!!

Answer 14

you might wanna help out your friend

Answer 15

http://openstudy.com/study#/updates/50384ef3e4b0b03bfb790953