Question

A company introduces a new product for which the number of units sold S is given by the equation below, where t is the time in months.

s(t)=155(7-9/(2+t))

a) Find the average rate of change of s(t) during the first year.
Which my answer was 1395/28

b) During what month of the first year does s'(t) equal the average rate of change?
I worked out the problem and got t to equal around 3.29, rounding that this would be the month of March. I entered that answer but the website didn't take that as correct. What could I have done wrong??

Answer 1

Part (a)
average rate of change is the difference between the end of last month to the beginning of the first month, divided by the number of months, so
Average=(s(12)-s(0))/12

Part (b)
Calculate the derivative of the function s(t), with respect to t:
d s(t) / dt
=d(1085-1395/(2+t))/dt
= 0 + 1395/(2+t)²
=1395/(2+t)²
by applying the power and chain rules.

Then equate the rate of change function (derivative) with the expression for the average over 12 months, which gives
1395/(2+t)²=1395/28

To solve for t, cross multiply and solve the quadratic for t, which should give two solutions, one of which is negative and to be rejected. The other should be between 0 to 12.

Post if you wish an answer check.

Answer 2

Got the same answer, 3.29 which is around march, but that answer was not correct according to the website