SOLUTION: 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? What is the largest value for the sales during the week? During wha

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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?
What is the largest value for the sales during the week?
During what week do we expect the sales to drop to zero?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
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:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2394 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.98978847012861, 12.9897884701286. Here's your graph: