Could someone please help me with this problem? I keep on getting the ln of a negative number when I solve, so no solution? But my math teacher says there is one....so confused. Thank you guys!
The sales S (in thousands of units) of a detergent after x hundred dollars is spent on ads are given by the formula $${\mathtt{S}} = {\mathtt{10}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{e}}}^{{\mathtt{kx}}}\right)$$ When $500 is spent on ads, 2500 units are sold.
a) Solve for k
b) Estimate the number of units sold if advertising expenditures are raised to $700.
+118723 $$x=5\qquad
S=2.5$$
befor i go any further are these the numbers you used?
+130511 OK...so we have
2.5 = 10(1 - ek5) divide both sides by 10
.25 = 1 - ek5 rearrange
ek5 = 1 -.25
ek5 = .75 take the ln of both sides
ln ek5 = ln .75 and by log property, we can write
k5 = ln.75 divide both sides by 5
k =ln.75 / 5 = -.0575
For $700 of expenditures, we have
S = 10(1 - e(7*-.0575) ) = about 3.3135 or about 3314 units
(Actually...I rounded "k"....the answer is really about 3315 units !!)
OHMAGOSH, THANK YOU MELODY AND CPHILL!!!
I was plugging in 2500 for S, so it came out as
2500 = 10 (1-e^(5k))
250 = 1-e^(5k)
249 = -e^(5k)
Then ln( -249) = e^(5k), where I got stuck.
But now that it is 2.5, everything makes sense now!
