Question 316385
S= -3.5n^2+42n+45. S=number of thousands of dollars of sales in week n.
When do you expect the sales to peak?
vertex gives you the max.
axis of symmetry:
n = -b/(2a) = -42/(2*(-3.5)) = -42/-7 = 6
It will peak at n=6 or the sixth week
.
What is the largest value for the sales during the week?
S= -3.5n^2+42n+45
set n=6
S= -3.5*6^2+42(6)+45
S= -3.5*36+252+45
S= -126+252+45
s= 171 (thousands of dollars)
.
During what week do we expect the sales to drop to zero?
set S = 0 solve for n:
S= -3.5n^2+42n+45
0= -3.5n^2+42n+45
Applying the quadratic formula yields:
n = {-0.99, 12.99}
We can toss out the negative answer leaving:
n = 12.99 weeks
.
Detail of quadratic follows:
*[invoke quadratic "n", -3.5, 42, 45 ]